I don't think there's enough of a market for an MLB network for the reasons you specified. ESPN is basically the MLB network in the summer, when it comes to lots of national games (I think they have to at least try to cover all 30 teams in the agreement), if people wanted the AFL and winter ball, I'm sure YES, NESN, and friends could find a few hours to put it.
The only national coverage that's really needed is October and a few games of the week on Saturday afternoons. In Fox's case, the Saturday games aren't wiping out ratings winners; that time is usually thrown to the affiliates to fill with Buffy or M*A*S*H reruns. I don't know what the other three do offhand, but it's never anything crucial, because most people are spending Saturdays in May and June outside enjoying the weather.