Some possible rationalizations:

Maybe...
Evil gods don't like rooms being sanctified, they're prefer everywhere to be cursed. Perhaps cursed rooms are typically tainted with evil, and removing that evil decreases the total level of evil in Thera. Maybe evil healers could get "taint room".

Evil gods are harsh and demanding and just don't really care if their followers get stuck up schit creak, and thus are not interested in handing out paddles.

As for neutral healers... well, maybe neutral gods are all just too aloof to grant those abilities. Sorry, I can't seem to come up with any good IC reasons for neutral healers not to sanctify rooms (especially since they don't get to use protection).

Note that I don't really agree with these rationalizations. I suspect that the real reasons are game-balance, and simple tradition held over from when healers were limited in alignment.

-Valkenar the Newbie, Poster of Uninformed Commentary.