Some aspects are always going to be subjective (eg. impact on quality of life or pain) and IMHO that's OK and we should absolutely attempt to measure them, not least because that information could help inform the treatment itself. Also, by measuring the changes in response over time for a patient, you can attempt to control for individual biases.
I agree that patient satisfaction surveys (in the UK, categorized as patient reported experience measures) can be very prone to bias and while important, are not necessarily correlated with outcomes.
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.
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.