For that to become an issue we'd have to introduce function body inheritance first. Indeed there is choice, but the choice is - to begin with - whether to introduce that concept or not (my vote on that matter is no).
For the class level, inheritance and overriding is already a fact, and there are observable effects whether or not "constant" should imply static binding. I think it should not: 1) It'd unnecessarily break the orthogonality principle, 2) it'd introduce a spurious difference wrt binding of function identifiers, 3) we'd have to introduce a new "nolocal" modifier, and 4) it'd massively break compatibility.