It sounds kinda analog to a one-time-pad vs. ordinary key encryption. Waiting for more "actual" entropy bits rather than stretching the existing entropy is lik

It sounds kinda analog to a one-time-pad vs. ordinary key encryption. Waiting for more "actual" entropy bits rather than stretching the existing entropy is like a one time pad, and it can (with a bit of effort, and assuming the integrity of the sources) guarantee similar security of the random generator to a one time pad. Stretching of the key means (at least in theory) that you could break the random function and predict the random series or your position in it. I guess your point of not worrying about ordinary key encryption should be applicable in an RNG context too and be similarly safe, though.