We haven't solved that underlying problem yet, and the problem isn't insurance. It's that many kinds of actor have motivations to misuse individual, detailed health data in ways that can be seriously harmful to the individual.
I don't know if there's a way to solve that problem, even in principle. It seems like an intrinsic conflict of interest thing.
Until that's solved, that will remain a major and rational reason why people care about health data privacy.
There's no point saying "ignore health data privacy and fix the real problem" until people can fix the real problem. Which as I've said, might not be possible even in principle.
Meanwhile, the thing people can do for themselve is focus on privacy of their healthcare records and demanding that be maintained. Institutions and companies can incrementally develop improvements to aggregating data that don't simply discard that privacy, like differential privacy for smart data aggregation, and zero-knowledge systems like the Google/Apple coronavirus alert system.
Perhaps eventually we'll and up with a way to aggregate health data in ways that are more helpful for diagnostics and population-level understanding of diseases, while safeguarding individuals from harmful consequences.