No it doesn't average out at all due to persistent differences in patient populations across providers which can't be adequately controlled for using the available data.
You misunderstand. You have a representative sample of the patients seen by that doctor. Individual differences like patient weight may be very important at the individual level, but across a thousands of people that's far less important than the overall differences across populations.
No that's simply not how it works and won't give you an accurate picture of quality differences between providers. I don't know how to make it any more clear.
Comparisons between providers is a separate issue.
Suppose you assigned people randomly to 101 doctors from 2 populations (A,B). Now suppose A was 10x as likely to die. D(0) get's 0% of A's and 100% B's. D(1) is 1A and 99B. All the way to D(100) that only get's B's.
In that admittedly simplified example you could determine that D(0) did a better job than D(100) by only getting 8x as many deaths even if 9.8x may be statistically irrelevant.
Yes, the real world is vastly more complex. But, while that may make a strict ordering impossible you can likely find out the best doctor is likely in the top quarter and the worst doctor very likely in the bottom quarter, which can be useful.
Picture a score card that said 80% chance in (0% - 20%], 15% chance in the (25%-50%], etc. That's not exactly meaningless information.
Nope that doesn't work because there's still no way to reliably control for the confounding factors. We don't even know what all the confounding factors are. Patients aren't randomly assigned to providers.
Sure, we don't have that information today. But, if we want to collect relevant information we could easily have a subset of doctors with random patient assignment. IMO, that's simply an implementation detail required if we want good information.
PS: US healthcare spending is over 3 trillion per year, rationally even minor improvements are worth large investments.