Because the compensation structure in Europe is vastly different than what we have here. You've spent the entire thread arguing against upending that.

No, I haven't. Why doesn't anyone get that? I'm not arguing for or against changing to a single payer system. I'm pointing out that the obstacles to making such a switch are not merely what The Powers That Be want, but also (and I think primarily) just basic political reluctance to inflict significant economic damage on large numbers of ordinary voters. I'm diagnosing, not advocating.

You won't ever get every single provider in the United States "into the same pool". There will concierge doctors who operate outside of any single payer system...unless you're willing to outlaw that and essentially force medical providers to work for the government. That's not going to fly on any number of grounds.

You don't have every single provider in Europe in the single-payer pool, either. There are always private doctors. Just not very many of them.

If you had a single-payer system that was funded through taxes, almost every doctor would be in it. Because almost every patient would be in it. You can't really compete with "free" - or to be more accurate, "zero marginal cost." If everyone has to pay taxes to fund the single payer system, and everyone can get medical care with no additional charge (or just a co-pay) in the single payer system, then no one's going to have private insurance any more. So almost every patient is going to be choosing between "free to me" and "paying market rate" for medical services. "Free to me" will win almost every time, so nearly all the doctors will be in the "free to me" pool.