At the moment I can't explain it with scientific precision. The reason to scrap the puzzles #161 to #256 isn't that #160 likely won't be reachable in our lifetime and this century. The reason is that hashing with RIPEMD160 caps the unambiguous bitrange to 160.

The relation private key --> public key is very likely unique, we can assume no collisions (I can't prove that mathematically, though), i.e. no two different private keys will give you the same public key.

To get a legacy public address there's a hashing step with RIPEMD160 that gives you a 160bit hash, thus there are mathematically obvious at max. 2¹⁰⁴ public keys with the same RIPEMD160 hash aka same legacy address.

Therefore by the initial puzzle conditions (no public key was revealed first), puzzles #161 to #256 make not much sense. This didn't occur to the puzzle creator at first but when he was nudged to it, he realized his mistake and redistributed funds from the no-sense range to the makes-sense range.

AFAIR revealing public keys for puzzles of multiples of 5 came even later (I could be wrong, don't have it crystal clear from my memory's bottom area).