I mean, Dodgers fans had to deal with this when Vin Scully was working for NBC. Ditto Giants fans when Jon Miller was on ESPN, Cardinals fans back when Jack Buck was the main guy for CBS, etc. Somehow they survived.
Benetti's Fox contract predates his Tigers one, and I imagine he has a limited number of dates where he can just blow off his network duties on short notice. I guess I really can't see that as being enough of a basis on which to judge his loyalty or commitment to the D.