As darth_pixel points out, people have had limited success with feeding multiple colors into a diamond hotend and mixing them, but I would argue this is not truly what you're looking for.
The problem is that when feeding multiple filaments into a diamond-style hotend, the colors do not naturally mix completely: if you look at an object printed this way the color changes with the angle you view it from.
This would not be fundamentally impossible to overcome: you could make the melt zone longer, and possibly introduce something to promote mixing (like a spiral path for the molten plastic). However, this would greatly increase the force required to extrude and make retraction near impossible. Both of these issues would reduce print quality.
The results would also not be very good, as you'd need a long purge between colors, limiting the number of distinct colors you can use in a single model while keeping the print time acceptable. Moreover, given how limited the resolution of FDM is you could not make very detailed graphics either.
Over all, you're much better served with painting or assembling parts printed in different colors.
Given the limited potential for color printing in FDM and the mentioned obstacles to building a color mixing hotend, I think it is natural nobody has built one (*) but that doesn't mean it is fundamentally impossible.
(*) There have been some attempts, many on Kickstarter, but none have been truly successful.