Alex, I’m sorry to contradict you on this …
It is not true that the delegator reward is independent of pool size. Instead, there is a cost to the delegator that varies considerably relative to pool size - the details are captured here.
It is so, because the a fix cost (i.e. what is removed from delegator rewards before distribution) divided by the total reward a given pool gets, is a much smaller fraction for large pools, than it is for small pools. We cannot contradict this simple mathematical truth.
This mechanism also helps that stake will eventually cluster around k saturated pools with k (very likely) being a lot less than number of blocks per epoch (i.e. k=500 now, it may be 1000 or even 10000 in the future, but not 21600). With k=21600 every pool would just make 1 block per epoch and there would be no economic reuse of compute resources.