There are many reasons, but some of the more cited ones are that (<>) will break less code than (++) would, since (++) is ubiquitous and (<>) is most used in some pretty printers. Yes, mappend's type can be refined to that of the current list (++), but the increased polymorphism still has the potential to break existing code by making it harder to resolve instances.
As for (<>) meaning not equal to, do you also have a problem with Monad's (>>) meaning a right bitwise shift, or the mutationey form of it, (>>=)? :) I don't think anyone in Haskell has ever used (<>) to mean (/=), so the fact that there exist a couple of languages out there that do use it that way shouldn't affect our decision.