Same reason why not having net neutrality is a problem. Eventually health care gets terrible for the people who aren't paying, or are paying less, and you've institutionalized a two or more tier public service based on wealth.

What if somebody could pay extra to have the best firemen, or the best police?

WalterBright has posed a real problem here, but I honestly think that the solution is just that patients pick their doctors, and if they can't get the doctor they want, they can get on a waiting list for that doctor while seeing another. Additionally, that waiting list would not involve any administrator latitude or patronage, just list seniority.

On the other hand, most health care is routine, and one doctor is as good as another. The best doctors are needed for the hard cases. A strict waiting list does not allocate doctors to where they would be most effective.

It's similar to the inherent misallocations of rationing - goods & services are not allocated to where they are most needed.

Because then the people who only get the baseline become a political force for how unfair that is. (We see this in the newspaper essentially every day regarding the public school system.)

Yet the doctors who charge outrageous sums may not actually be as good as the doctors everyone has access to at the county hospital. Indeed, teaching hospitals are known to have better outcomes, and serve the underserved.