The issue is autofocus. The slower systems, based on pixel contrast, can do the job purely from the main sensor, but if you want to do phase-detection autofocus (which all the big SLRs do, and which can give the focus computer magnitude and direction information for autofocus, thus yielding a faster lock), then you need a completely different design, where different pixels look at different parts of the lens.

Fuji has actually made a sensor that has phase-detection pixels stuffed amongst the regular pixels, giving you the best of both worlds without needing any sort of half-silvered mirror. (Instead, you get digital post-processing to fill in the blanks for the pixels that are used for focus instead of image capture.)