You can in fact "add whatever to the pool forever"

In the original statement you said that spewing a bunch of something does not benefit the adversary *at all*. The way I understood that was that the N-bit pool still has N bits of entropy. That's obviously not the case because the number of possible states goes down, and quick experiments with a really small toy HMAC confirm that (repeatedly running it causes the entropy to reduce from the original 16 bits to 8 or so, just as expected from the birthday paradox style configuration). To avoid that you need your primitive to be an (input-driven, obviously) permutation in the state space so that the number of states stays the same. There are constructions like this - IIUC, SHA3 uses one, unlike MD5/SHA1/SHA2 - but you need to pay attention to this.

On the other hand, for collision attacks N/2 is already the baseline due to the birthday paradox, so by itself this effect does not provide any improvements over that - a hash resistant to collision attacks would also be resistant to this effect.