You would definitely see more of a free market by producing fungible products with (hopefully) a bit less obfuscation. The insurance companies would still do their best to not cover a claim of course, so this is only a partial solution.

One nice side effect is that it's a small nudge in an organically 'designed' system rather than the inevitable chaos by changing the whole machine at once.

If you believe in single payer healthcare, it would be easy to attach redesigns in cash inflow to a set of standardized policies.

I've always admired the size of office staff in a doctor's office, no doubt mostly due to the complexity of the cashflow in the backend. Perhaps simplification of billing would result in less bookkeeping and more caregivers.