Many times what happens is that the "within" innovation is not so much innovation in itself, but the innovation is including aspects that were done by the avant-garde decades before, into a popular context.
avant-garde composers were playing with recording and editing techniques for a long time before the beatles came and used those ideas in a more catchy way, with a hairstyle to boot. The innovation is closer to the business side than to the music itself.
This is debatable to say the least. Lovers of the avant-garde commonly trot out the argument that there's just no room for genuine, transformative innovation within the mainstream that can be grokked by average folk, that it is played out in some sense. And lovers of mainstream music (and arguably mainstream culture more generally) routinely prove them wrong, by managing to innovate within those boundaries in a way that's genuinely compelling to many. It happens again and again.