Despite hip-hop's effects on the pop charts, we've yet to see the big networks really attempt to integrate rapping into their pop star competition shows, as Alyssa Rosenberg points out
...whether it's pop songs that include MCed bridges or hip-hop songs where the rappers are singing their own hooks or are bringing in pop stars to sing original hooks, hip-hop is increasingly embedded in the pop charts, even if it's not yet the dominant genre in American popular music. But the big competition programs tend to focus on the clarity of sung vocal performance. We haven't had a show yet that defines what makes a great MC, or defines an MC as the most important voice in American music.
Being the snob that I am, I really don't look forward to FOX defining that for America. But snobbery aside, I think a lot of this has to do with the relative youth of hip-hop. A sprawling musical genre rooted in spoken poetry is still a new thing to a lot of people. Singing your way to stardom, not so much. Because of that, I imagine a show like The Voice has the advantage of being family television and targeting a broad demographic.