昔は, 勉強しなくてもよかったものです is obviously correct. But apparently 昔は, (ねないでも,) 勉強しないでもよかったものです is not. The professor explained that this was because -なくてもいい is a set expression meaning "it's OK not to" or "it's OK even if (negative)" and that も (= also) can only be used with nouns otherwise. But this is a pretty unsatisfying explanation for me, because て-forms are treated in noun-like ways quite a bit (-てほしい, -てあげる, etc.) and so is -ないで in negative requests (-ないで下さい) and it seems kind of arbitrary that it can't be used with いい in this case.
Is it that:
1) -ないで can only modify verbs: 勉強しないで, いい点を取ったんです is ok but the above is not, because いい is an adjective.
2) Despite apparent similarities, -ないで and -なくて really are different parts of speech.
3) Something else? To be honest, I'm not even sure why it is that -ないで下さい is right when -なくてほしい is too.
Can someone with a more deeply linguistic knowledge of Japanese clear this up for me?