Yes, generic he can be used in the singular as well.

It is clearly valid. I personally don't care if others use "he" as a generic, but seeing at some people don't feel included when it is used, I increasingly use "they". Not least when I don't know someones preference, because I consider the most inclusive option to be the most polite.

I don’t feel included by they.

You objectively are, and in the choice of who to care about that means I have absolutely no interest in catering to people upset that others are included.

There’s no difference objectively between generic he and generic they. Both cover everyone. You just prefer one to the other. That’s fine, so do I.

There is an objective difference between generic he and generic they: In many contexts you can not tell whether the "he" was intended to be generic or not.