Baseball requires a lot more safety equipment. Even when played at the most casual level, the catcher needs body armor and the batters need helmets (of various sizes), so you need to have institutional support (or wealthy parents) to play baseball regularly. On top of that, girls (for whatever reason) generally don't have a lot of interest in playing baseball by the time (around puberty) when it becomes dangerous to play.

And baseball is incredibly difficult to play--essentially kids who are "good" at baseball have probably been playing their whole lives, so when the kids who played Little League (ages 4-10) quit for a few years, they can't keep up if they want to come back and start playing again at age 15. And that category covers pretty much all girls.

Softball (slow pitch in particular), on the other hand, can be played casually with little to no safety gear. You can bat without a helmet, and play catcher without body armor. So it's more accessible, whether to young girls, or grown men, or drunk lawyers.

So for the girls who want to play baseball, or something like it, softball provides at least an option. And if you're good at softball, then you move into the higher levels of competition, where you might be hitting balls that are moving just as fast (relatively speaking), and a great athlete, but softball is the only real choice.

You're asking why not just have girls play baseball instead of softball, I think the answer is as simple as "they don't want to" (generally speaking).

(And FYI, girls' basketballs are smaller.)