The mechanics of A/B testing math make implementing this a much less attractive proposition than you'd think it would be. I'm going to get handwavy but it will suffice for the moment: the amount of traffic you need to get statistical significance between N options grows at like O(N^2). How much of the color-space do you want to automatically converge over?

Most of my clients would struggle getting results at sufficient velocity with 10-way multivariate testing to say nothing of zomg-way multivariate testing.

Totally separate problem: Button color is far from the most salient thing you could be testing.