Gemcitabine and Cisplatin Without Cystectomy for Patients With Muscle Invasive Bladder Urothelial Cancer and Select Genetic Alterations

Inclusion Criteria: * Step 1 Patient Registration Eligibility Criteria * Histologically confirmed muscle-invasive urothelial carcinoma of the bladder. Urothelial carcinoma invading into the prostatic stroma with no histologic muscle invasion is allowed, provided the extent of disease is confirmed via imaging and/or examination under anesthesia (EUA). The diagnostic TURBT sample must have been obtained within 60 days prior to registration * 20 unstained slides (10 micron thickness) of formalin-fixed paraffin-embedded (FFPE) pre-treatment diagnostic transurethral resection (TUR) specimen available (for sequencing), with 2 (5 micron) slides at the start and end of the 20 slides, for a total of 22 unstained slides. An FFPE block is also acceptable * Clinical stage T2-T4aN0/xM0 disease * Medically appropriate candidate for radical cystectomy as assessed by surgeon * No concomitant multifocal carcinoma in situ; a single focus is allowed * A single muscle-invasive bladder tumor measuring ≤5 cm in size as defined by the surgeons at cystoscopic evaluation. When documented, pathologic size at cystoscopy and TURBT will take precedence over radiographic measurements of tumor size. * No clinical or radiographic evidence for locally advanced or metastatic disease * No prior anti-PD-1 or anti PD-L1 therapies, or systemic chemotherapy within the past 5 years (prior intravesical induction immunotherapy for non-muscle invasive disease is allowed, defined as BCG x6 doses and maintenance therapy); BCG refractory disease, defined as disease recurrence within 3 months of BCG therapy, is not allowed. Intravesical chemotherapy is allowed. * No prior radiation therapy to the bladder or prostate * No major surgery or radiation therapy =\< 4 weeks of registration (TURBT is allowed). * Not pregnant and not nursing. This study involves an agent that has known genotoxic, mutagenic and teratogenic effects. For women of childbearing potential only, a negative pregnancy test done =\< 14 days prior to registration is required * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Calculated creatinine clearance ≥ 55 mL/min using formula per institutional standard or investigator's discretion. The same formula should be used to calculate all subsequent creatinine clearances. * Total bilirubin =\< 1.5 x upper limit of normal (ULN) \* (For patients with documented Gilbert's syndrome Total Bilirubin =\< 3 x ULN) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x ULN * No evidence of New York Heart Association (NYHA) functional class III or IV heart disease * No ongoing cardiac dysrhythmias of National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade \>= 2 * No pre-existing sensory grade \>= 2 neuropathy * No pre-existing grade \>= 2 hearing loss * No serious intercurrent medical or psychiatric illness, including serious active infection * None of the following within the 6 months prior to study drug administration: myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebrovascular accident, or transient ischemic attack * No known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness or other active infection. HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with the drugs used in this trial. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy, when indicated * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to the agents used in this study * No concurrent treatment on another clinical trial; supportive care trials or non-therapeutic trials (e.g., quality of life) are allowed * No prior malignancy except for: adequately treated basal or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for five years. Patients with localized prostate cancer who are being followed by an active surveillance program are also eligible * Step 2 Patient Registration Eligibility Criteria * Patients must have completed 4 or more cycles of protocol-directed chemotherapy and DDR gene results must be available * Step 3 Patient Registration Eligibility Criteria (only patients with a DDR gene alteration) * Deleterious alteration within 1 or more of 9 pre-defined DDR genes within the pre-treatment TURBT deoxyribonucleic acid (DNA) * Cystoscopy and imaging performed to determine stage/treatment assignment