Health care systems around the world are facing mounting pressure as demand rises and resources fall short. Years of underinvestment, staffing shortages, and recruitment challenges are colliding with the needs of aging populations that require more frequent and complex care. The result is increasingly uneven access, fragmented patient experiences, and exhausted clinicians struggling with stress and burnout. Agentic AI is emerging as a potential way to ease that burden—not by replacing health professionals, but by helping them work more efficiently and focus on patients. By coordinating tasks, supporting decision-making, streamlining administrative work, and improving access to services, agentic AI could help health systems become more responsive and humane. As the crisis deepens, the technology may play a key role in rebuilding care around people rather than paperwork.