My music teacher back in middle/high school told us straight in our face why atonality didn't succeed, it sucks. And he proved to be right.
Well, I wouldn't simply say that, but the human ear is atuned to pick up patterns in music, and these patterns of notes and intervals form keys, meaning that while you can get some very nice pieces which are essentially atonal (Satie's gynopedies and gnossiens technically are though like all atonal music they could be described as a series of phrases in constantly shifting keys), there's a very limited amount of notes you can have being played at one before it just becomes a wall of noise rather than music. Not to mention that it's damn near impossible to hold a tune to.
So I'd say this isn't really possible because the way how the brain is built means that as a general rule people find tonal music more pleasing and as it can be sung to far more easily, the tonal pieces will inevitably be more succesful financially and more popular in terms of what people want to hear.
Now, this doesn't mean you can't have more atonal music, but you can't get the majority of music to be atonal.