Definitely, but I think implementing a nice trait system first would be substantially easier. Rewriting Base to take advantage of it everywhere would definitely be breaking and would also be a lot harder.
That, however, may be where the bar is now. (Not the breaking part—the art would be doing what can be done without being breaking—but in terms of “a lot of work”.) Now that we’re in the 1.x stable release series, there’s well-justified reluctance to substantial new features without there being a “consumer”: how else do you know whether you’ve gotten the design right, and that the change yields real benefits without causing problems elsewhere? Surely you’ve noticed this in the discussion of https://github.com/JuliaLang/julia/pull/24990? This is kind of a more refined version of Julia is not at that stage of development anymore–deep changes are now harder. That’s the price of Julia’s success!