Baseball already has this restriction, among others (depedning on the league or tourney), so we know how it will play out. And that is:
#3: coaches develop more pitchers.
As Greenmonsters said, how many girls give up on pitching because they know they aren't going to get a chance? I'd bet more would stick with it if they knew they were going to pitch even just a couple of innings every third or fourth game. And coaches would spend the time working with them because they'd need them to pitch.
I think it is a bit easier with baseball. Even if you have never pitched before you can go to the mound and pitch in baseball. Not quite the same with softball. The problem is that quality PC's are few and far between and unlike baseball, most fastpitch coaches will not even attempt to develop a pitcher. Even though pitching is the heart and soul of a team, most coaches leave that to the parents via PC. Even many top college programs do not have a dedicated pitching coach.