Intensity Modulated Proton or X-Ray Therapy After Surgery for Treatment of Head and Neck Cancer, the HEADLIGHT Study

Inclusion Criteria:

* Age \>= 18 years
* Histological confirmation of a newly diagnosed non-human papillomavirus (HPV) associated malignant epithelial cancer in the head and/or neck. Diagnosis requires confirmation of p16 and/or HPV DNA negativity for oropharyngeal and unknown primary sites. p16 positivity in skin cancers is allowed
* Primary lesion located in the nasal cavity, paranasal sinuses, oral cavity, oropharynx, larynx, hypopharynx, salivary glands, lymph nodes (unknown primary or metastasis from head and neck \[HN\]-skin primary) or skin cancer where lymph node radiation is recommended

  * NOTE: Patients with primary lesions in the larynx must have a T3 primary, bulky T2 primary (\> 6 cc), and/or at least 1 regional lymph node
* Confirmation of American Joint Committee on Cancer (AJCC) 8th edition defined M0 established by positron emission tomography (PET)/computed tomography (CT) or PET/magnetic resonance imaging (MRI)
* Eastern Cooperative Oncology Group (ECOG) performance status (0-1 prior to initial treatment)
* Able to provide written informed consent
* Able to complete questionnaires independently or with assistance
* Willing to return to enrolling institution for follow up during the observation phase

Exclusion Criteria:

* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy

  * NOTE: Patients known to be HIV positive, but without clinical evidence of immunocompromised state, are eligible for this trial
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Other active malignancy =\< 2 years prior to registration

  * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix and prostate cancer with a Gleason score of 6 or less
  * NOTE: If there is a history or prior malignancy, they must not be receiving ongoing anticancer treatment
* History of myocardial infarction =\< 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias
* Prior radiation therapy that would have a clinically significant overlap with the intended head/neck radiation
* For Arms A and B only: Unable to receive proton therapy because of extensive metallic hardware in close proximity to treatment site, logistical circumstances, or any other reason
* Any of the following diagnoses: HPV-associated squamous cell carcinoma, germ cell tumors, hematologic malignancies, neuroendocrine malignancies, adenoid cystic carcinoma, sarcomas of bone, benign tumors