Medical education faces challenges in providing scalable, consistent clinical skills training. Simulation with standardized patients (SPs) develops communication and diagnostic skills but remains resource-intensive and variable in feedback quality. Existing AI-based tools show promise yet often lack comprehensive assessment frameworks, evidence of clinical impact, and integration of self-regulated learning (SRL) principles. Through a multi-phase co-design process with medical education experts, we developed MedSimAI, an AI-powered simulation platform that enables deliberate practice through interactive patient encounters with immediate, structured feedback. Leveraging large language models, MedSimAI generates realistic clinical interactions and provides automated assessments aligned with validated evaluation frameworks. In a multi-institutional deployment (410 students; 1,024 encounters across three medical schools), 59.5 percent engaged in repeated practice. At one site, mean Objective Structured Clinical Examination (OSCE) history-taking scores rose from 82.8 to 88.8 (p < 0.001, Cohen's d = 0.75), while a second site's pilot showed no significant change. Automated scoring achieved 87 percent accuracy in identifying proficiency thresholds on the Master Interview Rating Scale (MIRS). Mixed-effects analyses revealed institution and case effects. Thematic analysis of 840 learner reflections highlighted challenges in missed items, organization, review of systems, and empathy. These findings position MedSimAI as a scalable formative platform for history-taking and communication, motivating staged curriculum integration and realism enhancements for advanced learners.