It would be better for all (exceptCBS) if basketball started in December (the end of the football season) and lasted until April. Sure, it would go up against the first round of the NBA playoffs, but I don't think that would cut into the ratings very much.
However CBS has the rights, and the crown jewel ofCBS Sports is the Masters. Nothing is going to interfere with detract from that event. I feel certain that the NCAA is contractually bound to finish its tournament before the Masters starts.
Starting a month later:
(a) would not hurt NCAA football;
(b) would assist women's basketball, because it's finals would not be the same weekend was the men"s; and
(c) would help men's basketball because it's first month would not be overshadowed by NCAA football
and there would be less of an overlap with the NFL.
But it won't happen.