Radiation Therapy and Cisplatin With or Without Surgery in Treating Patients With Stage III-IV Oropharyngeal Cancer

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of squamous cell carcinoma of the oropharynx, localized to the tonsil, glossopharyngeal sulcus, and tongue-base within 6 weeks (42 days) of registration * The primary tumor must be resectable through a transoral endoscopic head and neck surgery with anticipation of resection free margins (resection does not require total or subtotal glossectomy or total laryngectomy); specifically, patients must (1) not have trismus, (2) not have interincisor opening less than 2.5 cm, and (3) not have poor transoral exposure of the tumor itself nor surrounding soft-tissue margins, regardless of etiology * Clinical stage III-IV; T1-2, N1-2b; T3, N0-2b, with only well-lateralized exophytic T3 tumors not approaching within 1 cm of midline, and amenable to transoral eHNS * p16 protein (p16) negative by immunohistochemistry (documented by the institution's pre-enrollment biomarker screening at a Clinical Laboratory Improvement Amendments \[CLIA\]-certified lab), defined as absent, weak, and/or only focal nuclear and cytoplasmic staining in less than 70% of the tumor cells * Appropriate stage for protocol entry, including no distant metastases or adenopathy below the clavicles, based upon the following minimum diagnostic workup: * History/physical examination by the treating physician (radiation oncologist, medical oncologist, or head and neck surgeon) within 30 days prior to registration * Imaging of the head and neck (CT with contrast, positron emission tomography \[PET\]/CT, and/or magnetic resonance imaging \[MRI\]) within 30 days prior to registration; a CT scan with contrast is mandatory (unless contraindicated, e.g. contrast allergy, etc.); note that a PET/CT scan alone (unless performed with contrast) is not sufficient * Chest CT scan (with or without contrast) or PET/CT of chest (with or without contrast) within 30 days prior to registration * Modified barium swallow (MBS) to assess swallowing function within 30 days prior to registration * Preoperative Mallampati assessment as documented by attending surgeon within 30 days prior to registration * Zubrod performance status 0-1 within 30 days prior to registration * Absolute neutrophil count (ANC) \>= 1,800 cells/mm\^3 based upon complete blood count (CBC)/differential * Platelets \>= 100,000 cells/mm\^3 based upon CBC/differential * Hemoglobin \>= 8.0 g/dl based upon CBC/differential (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 8.0 g/dl is acceptable) * Total bilirubin =\< 2 mg/dl * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \< 3 x the upper limit of normal * Serum creatinine =\< 1.5 mg/dl and/or creatinine clearance (CC) \>= 50 ml/min; CC can be determined by 24-hour collection or estimated by Cockcroft-Gault formula * Serum pregnancy test within 14 days prior to registration for women of childbearing potential * Women of childbearing potential and male participants who are sexually active must practice medically effective contraception during treatment and for 42 days following completion of treatment * Patient must be able to provide study-specific informed consent prior to study entry Exclusion Criteria: * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 1095 days (3 years) (for example, carcinoma in situ of the breast or cervix are all permissible) * Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields * Severe, active co-morbidity, defined as follows: * \> 2 based on the American Society of Anesthesiologists (ASA) physical status classification system * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Transmural myocardial infarction within the last 6 months * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days before registration * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects * Acquired Immune Deficiency Syndrome (AIDS) based upon current Centers for Disease Control (CDC) definition; note, however, that human immunodeficiency virus (HIV) testing is not required for entry into this protocol; the need to exclude patients with AIDS from this protocol is necessary because the treatments involved in this protocol may be significantly immunosuppressive; protocol-specific requirements may also exclude immuno-compromised patients * Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception; this exclusion is necessary because the treatment involved in this study may be significantly teratogenic * Prior allergic reaction to cisplatin * Radiographic evidence of retropharyngeal metastasis