That makes sense, yes using all the quantiles from 0:0.01:1 as equally important means you will need to go deep into high sample size before the distance metric itself is asymptotically anything… The 1% and 99% quantiles are high variance for example.
In essence fitting an entire distribution is an infinite dimensional problem, and there doesn’t exist an asymptotic sample number when the dimensionality is infinite. Of course in this case you’ve restricted it to a 100 dimensional finite dimension approximation, and eventually you’d get to an asymptotic range, but I imagine for that model the asymptotic range is well above 5000 samples.