if you remove a small (...) part of the input space, you’re still going to end up with the same amount of possible hashes.

The number of "possible hashes" does not enter into it. It is the input space that the hacker needs to iterate, not the hash space.

That is to say, the hacker needs to find an input that when hashed, matches the hash in question. Smaller the input space, the less work he has to do.