Testing the Addition of MEDI4736 (Durvalumab) to Chemotherapy Before Surgery for Patients With High-Grade Upper Urinary Tract Cancer

Inclusion Criteria: * STEP 1 REGISTRATION AND RANDOMIZATION * Patients must be \>= 18 years of age * Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible * Patient must have a diagnosis of high grade upper tract urothelial carcinoma expected within 14 weeks (98 days) prior to registration/randomization with one of the following: * Biopsy (gold standard, preferred) and either upper urinary tract mass on cross-sectional imaging or * Tumor directly visualized during upper urinary tract endoscopy * High grade cytology and clinically estimated invasive upper urinary tract mass on cross-sectional imaging (e.g., including presence of tumor-related hydronephrosis) or tumor directly visualized during upper urinary tract endoscopy * NOTE: Universal histologic testing of UTUC with additional studies, such as immunohistochemistry or microsatellite instability, is strongly recommended to identify patients with high probability of Lynch-related or other germline mutation related cancers whom clinicians should refer for genetic counseling and germline testing (this is not required for eligibility) * Due to the anatomy of upper urinary tract and lack of muscularis propria, pathologic evidence of cT2 on biopsy is usually not possible * Leukocytes \>= 3,000/mcL (obtained =\< 14 days prior to registration/randomization) * Platelets \>= 100,000/mcL (obtained =\< 14 days prior to registration/randomization) * Total bilirubin =\< 1.2 mg/dL (or ≤ 2 mg/dLfor patients with Gilbert's disease) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2 x institutional ULN (obtained =\< 14 days prior to registration/randomization) * Hemoglobin (Hgb) \>= 9 g/dL (obtained =\< 14 days prior to registration/randomization) * NOTE: Packed red blood transfusion is allowed to achieve this parameter as per treating investigator * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months prior to registration/randomization are eligible for this trial * NOTE: These patients must be stable on their anti-retroviral regimen with evidence of at least two undetectable viral loads within the past 6 months on the same regimen; the most recent undetectable viral load must be within the past 12 weeks. They must have a CD4 count of greater than 250 cells/mcL over the past 6 months on this same anti-retroviral regimen and must not have had a CD4 count \< 200 cells/mcL over the past 2 years, unless it was deemed related to the cancer and/or chemotherapy induced bone marrow suppression. They must not be currently receiving prophylactic therapy for an opportunistic infection and must not have had an opportunistic infection within the past 6 months * NOTE: For patients who have received chemotherapy in the past 6 months, a CD4 count \< 250 cells/mcL during chemotherapy is permitted as long as viral loads were undetectable during this same chemotherapy. They must have an undetectable viral load and a CD4 count \>= 250 cells/mcL within 7 days of registration/randomization * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * NOTE: Testing for HIV, hepatitis B or hepatitis C is not required unless clinically indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and have undetectable viral load. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * Patient must have a body weight of \> 30 kg * Patient must have life expectancy of \>= 12 weeks * Patient must have creatinine clearance \> 15 ml/min as estimated by Cockcroft-Gault formula or glomerular filtration rate (GFR) \> 15 ml/min/1.73m\^2 within 28 days prior to registration/randomization * NOTE: Patients will be assigned to cisplatin-ineligible and cisplatin-eligible cohorts based on their creatinine clearance, Eastern Cooperative Oncology Group (ECOG) performance status, and grade (if any) of peripheral neuropathy and/or hearing loss in keeping with recommended cisplatin contraindications. Patients who are cisplatin-eligible will be randomized to either Arm A or Arm B and patients who are cisplatin-ineligible will be registered to Arm C * Patients that meet any of the following four criteria will be registered to the cisplatin-ineligible Arm C if they meet other eligibility criteria: * Creatinine clearance \> 15 ml/min and =\< 50 ml/min (estimated by Cockcroft-Gault formula) or GFR \> 15ml/min/1.73m\^2 and ≤ 50 ml/min/1.73 m\^2 * Hearing loss \>= 3 * Neuropathy \>= 2 * ECOG performance status 2 * In addition, the patient must have an absolute neutrophil count (ANC) \>= 1,000/mcL obtained =\< 14 days prior to registration * Patients that meet all of the following four criteria will be randomized to the cisplatin-eligible Arm A or Arm B: * Creatinine clearance of \> 50ml/min (estimated by Cockcroft-Gault formula) or GFR \> 50ml/min/1.73m\^2 * ECOG performance status 0-1 * Hearing loss grade 0-2 * Neuropathy 0-2 * In addition, the patient must have an absolute neutrophil count (ANC) \>= 1,500/mcL obtained =\< 14 days prior to randomization * Also, the patient must have left ventricular ejection fraction (LVEF) \>= 50% by (either multigated acquisition scan \[MUGA\] or 2-D echocardiogram) obtained within obtained within 28 days prior to randomization Exclusion Criteria: * Patients must not have any component of small cell/neuroendocrine carcinoma. Other histologic subtypes (variants) are permitted provided the half or predominant (\>= 50%) subtype is conventional urothelial carcinoma * Patients must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used. All patients of childbearing potential must have a blood test or urine study within 14 days prior to registration to rule out pregnancy. A patient of childbearing potential is defined as any patient, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Patients of childbearing potential and sexually active patients must not expect to conceive or father children, either by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse from the time of registration, while on study treatment and for at least 6 months after the last dose of protocol treatment * Patients must have no evidence of metastatic disease or clinically enlarged regional lymph nodes (\>= 1.5 cm short axis) on imaging required within 28 days prior to registration (Non-regional findings \>=1.5 cm short axis that in the opinion of the investigator are not concerning for involvement based on radiographic characteristics, chronicity, avidity on positron emission tomography (PET) or other imaging or other criteria can be eligible based on investigator discretion). * NOTE: Patients with elevated alkaline phosphatase, calcium or suspicious bone pain/tenderness can also undergo baseline bone scan to evaluate for bone metastasis at the discretion of local provider. * Patient must meet below criteria for prior/current malignancy history: * Non-urothelial cancer malignancy history: * Patient must not have another active (or within two years) second malignancy other than resected non-melanoma skin cancers, resected in situ breast, cervical or other in situ carcinoma, and either clinically insignificant per the investigator (e.g. =\< Gleason 3+4) on active surveillance (or watchful waiting) or previously treated prostate cancer with no rising prostate specific antigen (PSA) and no plan to treat * NOTE: Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Urothelial cancer malignancy history: * Patient may have a history of resectable urothelial cancer as long as patients meet one of the following: * T0, Ta or Tis at any time * T1-4a N0 and no evidence of disease (NED) for more than 2 years from the latest therapy \[e.g., radical surgery, transurethral resection of bladder tumor (TURBT), radiation, chemotherapy (neoadjuvant or adjuvant, or with radiation)\]. Prior immune checkpoint inhibitor is not allowed. * Patient with history of \>= pT4b, N+, and/or M1 UC is not eligible. * NOTE: Patients in whom concomitant or prior bladder/urethra predominant (\>= 50%) urothelial carcinoma have been surgically resected and demonstrated to be only Ta or carcinoma in situ (CIS) (\< cT1 N0) are eligible regardless of time elapsed * Patient must not have any uncontrolled illness including, but not limited to, ongoing or active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis \[TB\] testing in line with local practice), symptomatic congestive heart failure (CHF), myocardial infarction (MI) or unstable angina pectoris, significant uncontrolled cardiac arrhythmia, clinically relevant liver cirrhosis, interstitial lung disease, or psychiatric illness/social situations in the three months prior to registration that would limit compliance with study requirements * Patient must not have received prior radiation therapy to \>= 25% of the bone marrow for other diseases * Patient must not have received prior systemic anthracycline therapy * NOTE: Patients who have received prior intravesical chemotherapy at any time for non-muscle invasive urothelial carcinoma of the bladder are eligible * Patient must not have either history of or active autoimmune disease requiring immunosuppressive therapy within 2 years prior to registration/randomization or any history of inflammatory bowel disease (inflammatory bowel disease \[IBD\], e.g. ulcerative colitis, or Crohn's disease), neuromuscular autoimmune condition, immune-related pneumonitis or interstitial lung disease. Patients with well-controlled hyper/hypothyroidism, celiac controlled by diet alone, diabetes mellitus type I, vitiligo, alopecia, psoriasis, eczema, lichen planus, or similar skin/mucosa condition are eligible * Patient must not be on or have used immunosuppressive medication within 14 days prior to the first dose of durvalumab. The following are exceptions to this criterion: * Intranasal, inhaled, intra-auricular, topical steroids, or local steroid injections (e.g. intra-articular injection * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent at the time of enrollment * Steroids as pre-medications for hypersensitivity reactions (e.g. computed tomography \[CT\] pre-medication) * Patient must not have received live attenuated vaccine within 30 days prior to the first dose of durvalumab, while on protocol treatment and within 30 days after the last dose of durvalumab * Patient must not have had a major surgical procedure within 28 days prior to registration/randomization * NOTE: Cystoscopy/ureteroscopy, stent placement or nephrostomy tube is not considered major surgery * Patient must not have history of allogenic organ transplantation