Cholelithiasis is a common surgical disorder creating a high burden of the healthcare system. The introduction of minimally invasive technologies justifies the shift towards hospital-replacing models, but the institutional aspects of their use in the metropolis are still poorly understood. The study aimed to assess the role of hospital-replacing technologies in organizing elective surgical care provision to patients with cholelithiasis based on the retrospective analysis data for the years 2016–2025. A retrospective observational study was conducted based on the aggregate data of the Moscow City Health Department. The dynamics and structure of elective cholecystectomy procedures, the development of the short-stay unit (SSU) network, length of hospital stay, and age distribution were analyzed. The number of laparoscopic cholecystectomy procedures increased by 48%, the number of open surgical interventions decreased by 93.4%. The SSU network expanded from 5 to 30 units, the share of surgery due to cholelithiasis performed at the SSU reached 40.2% relative to the year 2016. The SSU stay was associated with the 75.0% bed-day reduction (to one day) and the actual hospital stay reduction by more than 80.0% (to 16.2 ± 7.4 h) compared to the round-the-clock hospital (RCH). Age differences (the share of patients over the age of 70 was 13.3% in the SSU vs. 36.0% in the RCH) support selective routing of patients at lower risk to the SSU. Conclusions: SSU has become an important organizational instrument of elective surgery due cholelithiasis that has ensured a sharp patient treatment time reduction over the preceding 10 years.