Capitalism doesn't become "not capitalism" because practitioners need to be licensed and public safety and/or public opinion demands regulations be put in place.
If someone recommends "don't do that" and you do that anyway, you can't reasonably blame their advice for being wrong because things went wrong when you did the thing anyway and then justify it with "well, sometimes people don't listen to your advice, so clearly it's not good enough, we really need to do more of the thing you advised against to fix this."
Are you saying that capitalism means completely open, zero regulation, zero licensure markets? Because it absolutely does not. It means (among other things) a competitive market with minimal information asymmetries between producer and consumer. Regulation can at time help this, e.g. requiring information disclosure, or preventing monopolistic practices.
Just because a lot of regulations are bad (or enforced poorly) and some licenses are onerous does not mean "regulation === bad" or "licensure === bad."
You're arguing against an extreme position I have not advocated for.
But when bad regulations cause bad outcomes, it's pretty weird to focus the blame on the people warning that bad regulations can cause bad outcomes instead of how the regulations are flawed and whether they can be fixed.
If your intent is to capture the market so that you can set the price, that is not capitalism. If licenses are limited, then the amount any one business can own should be limited. Having the ability and using it to artificially limit competition is called a cartel and should be illegal in the USA. An artificial limit on the amount of competition allowed <> capitalism.
See taxi medallions. Another example for a long time would have been FAA approval of new aircraft type certificates and the requirements creating a huge barrier for entry to get them that artificially prevented competition.
Capitalism kind of does become "not capitalism" when a small cartel of individuals uses these public safety rules to arbitrarily cap the number of professionals who can be certified. At that point, you have something approaching mercantilism. Rules can be good for markets, but in the medical industry in the US they are far past that point.
I haven't checked, but I assume that today there are more rules and regulations on doctors in the US than there were on the entire Soviet economy. Some of those rules are good, but most of them are in place because a hospital system or a medical association lobbied to put them in place so that they could keep barriers to entry high.
