You can't use the GPL for an entire distribution. You could argue that it's possible to only package GPL-compatible software and sublicense all of it under the GPL. This is impractical because of MPL and LGPL libraries. But even then the distribution isn't under the GPL, so you could inject an "MIT version" of musl and other non-GPL versions of the rest of the software.

tl;dr: That's not how licenses work.

There have been some interesting questions about packaging Ubuntu and their terms of use. I always found their terms of use odd, because they are basically reinstating trademark law inside a software license.