Allow doctors to be "certified" by private organizations, then watch how quickly medical schools change, residency allotments open up, and doctor ranks swell. As the supply of seats in medical schools and number of residencies rises, the cost of medical school will decrease. More doctors with less debt will put downward pressure on medical prices.
You may argue that quality would not increase under such competition, but I disagree. People who can't afford healthcare would be able to afford poor quality healthcare which is better than they currently enjoy. Rich people will still have vanity certified doctors. In general the cost of comparable quality healthcare would be lower.
TLDR; don't complain about disappointing results of competitive pressure in a market with very limited competitive pressure.
That's because there really isn't any competitive pressure. Not for consumers anyway. The way our healthcare is tied to our employment means we get little choice in providers ourselves, leaving that decision to our employers, who probably don't have our best interest at heart.
We know that that has been true in many cases, but we don't know that it always will be true in all cases. For example, I don't think there's a very good argument that competitive pressure has led to a super high quality healthcare system in the US vs. the rest of the industrialized world. Competitive pressure optimizes for certain things, and those things are not always what is best for the public. Especially, if "competitive pressure" is applied by a trust, it can cause market failures.
I don't know that Amazon is that. Maybe it will be. But, last I checked, we do still have ground floor retail. I think there's an equilibrium that we'll reach at some point, where retail space commands lower rents and has to provide a high quality shopping experience. The Best Buys of the world are done for, but the Nordstroms are not.