I support affordable universal access to basic healthcare regardless of ability to pay, but you're overestimating the impact of the healthcare system. Up until a few generations ago there was no real "system" at all, and treatments frequently caused more harm than benefit. This wasn't a significant cause of violent revolutions.

Even today, organized healthcare beyond vaccines and antibiotics has only a marginal impact on lifespan and healthspan. It's way behind sanitation (clean drinking water, sewage systems, waste disposal) and lifestyle issues (substance abuse, obesity, lack of exercise).