Medical care has (strongly) diminishing returns. For a given investment, the return is much higher by investing in those who receive little to no medical care, instead of investing further in those who already have good medical care.
You're saying that in a fully governmental medical system, there's a risk that a few people who get only good care, but could avoid paying out-of-pocket for excellent care, are worse off. Countries with universal healthcare don't typically have any rules prohibiting buying additional care for yourself though, so this is largely a strawman.
I've not seen anyone claim that the medical care available to those with money in USA is a disgrace. The part that is disgraceful is at the other end of the scale.