Some girls play regular baseball, but institutionally, girls are pushed towards softball. The only difference I can see between softball and baseball is the size of the ball and the underhand vs. overhand pitch. Are there other differences that cause the girl/boy distinction make more sense?
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At a younger age, girls are able to keep up with boys on the baseball field. As they hit puberty, boys become too powerful to compete with. So many young women switch to playing softball. Which, because of Title IX, can provide them with college scholarships to play softball.
As far as why women don't play women's baseball rather than women's softball? I'm sure that there was a sexist reason for it back in the past. A Softball is larger and softer than a baseball and probably was seen as being more suitable for women.
At this point, it doesn't matter. Softball affords young women to get scholarships and get a college education. Which is a good thing.