Well, actually, Tox also believes it's about psychology, but I don't really believe in that. The second reason, which I think is more important, is for information.
If we execute Mirka now, and the Mafia ends up on an unprotected Mirka, and the Town misses, then even without killing Ray, the city is already lost.
Added after 57 seconds
But according to Yashur, he's revealing Mirka.