It looks like -Weverything for gcc would make a lot of code not compile (along with -Werror). For example, it would include -Weffc++, right? Those are warnings if your code just doesn't obey one guy's now-outdated opinions of what C++ should look like.
Yes, -Weverything + -Werror is often a silly combination. That isn't a GCC-specific problem, though. Clang with both flags will fail to compile quite a lot of code, too.
As the other reply points out, you can just use -Wno-effc++ on top of -Weverything. You could also avoid that particular problem by not using C++ ;-).
The actual reason why -Wall doesn't include more warnings is because too many people rely on the fact that -Wall includes warnings for questionable code that is easy to avoid. It's a bad name, but it's not being changed any time soon.