I did the usual: have a look at all the challenges.
I agree that using the tag for challenges which request a function (instead of a program) is useless. And this is how most challenges used the tag.
But there is a valid use case for having such a tag: for all challenges that actual deal with functions (as objects), e.g. challenges about higher-order functions or which are otherwise related to functional programming or programming-puzzles relating to functions. This is no different from the string or number tags.
So far, there are two challenges like this (with the tag):
Additionally, it's a good tag to have for tips questions about functions in particular. There is one of those so far:
We should keep a tag for these cases, but I wouldn't be opposed to making a new one called functions instead (note the plural). Otherwise, I suggest that we rewrite the tag wiki and excerpt for function tag, to clarify that it should not be used, just because the challenge asks for a function - and then remove the tag from the other 17 questions, and leave it on the three mentioned above.
As Peter mentioned, there's already a functional-programming tag. We could either use that instead of functions (although the latter is probably a bit more general), or we could also subsume those four questions under a new functions tag. In any case, I'd rather not have both, because it will lead to no end of confusion about which tag to choose for some questions.