Well the thing is, if you have a child, why would a mother abandon her child to do whatever she's doing in the game? It would have to be an extremely important reason. As progressive as society may be, I imagine at least a super-majority of people would agree that if a child had to be raised by a single parent, given that the parents are equally responsible (and often times, even if they aren't), the mother is the preferred choice.

Fathers often go to war, go to work every day, it makes more sense for them to be absent, because it happens very frequently all across the world, and the system doesn't seem to be broken. Single mothers are extremely common, single fathers are extremely uncommon.

While video games don't have to represent reality, they still kinda do. A mother choosing to abandon her family/child to fight crime or whatever just doesn't really make sense to us as a species at this time. I think it would just come off as hamfisted pandering to third wave feminism to most of the audience, which kinda turns people off.