I'm mostly familiar with the UK system, but medical professionals make pretty much all the decisions here, with a large degree of discretion according to their professional judgement (and they never have to adjust or delay their care based on whether you can pay). Except for some particularly expensive treatments (think CAR-T for cancer) which are not available at all in the state funded system. But you can still pay for those privately if you want to.
We could just not do that. If you change the flow of control certain problems solve themselves. Think about a landscape where government funding multiplies the patient dollar, for example.