I would humbly suggest that this question is sort of like asking "why aren't football and Rugby played the same way?" They are played differently because they are different sports.
Assuming you are talking about fast-pitch softball, it is interesting to ask, "why does fast-pitch softball exist as a sport?" Softball apologists suggest that it's just as hard to hit an underhand softball from the shorter distance than to hit an overhand Baseball from 60 feet 6 inches.
Why are they different? Because they have different rules. They are different games. Why did softball come about is another question. It's possible it hung around as a variant of baseball which originally dictated underhand pitching of the ball. The rules changed to allow overhand throws from the mound so perhaps some people kept playing with the original underhand rule and the game evolved from there.
Opinion
The main reason for the differences in the rules is due to the size of the ball used. I think the most interesting thing to know would be, "Why is it that baseball is mainly designated for men and softball generally speaking is designated for women? (other then recreation leagues)
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The pitcher's mound is not elevated at all.
(if not professional league mound can be elevated)
mound is closer than baseball mound, also there is no grass in the infield
no. different sized balls and bats field differences under hand pitching motion and all dirt infields
Baseball is played with a smaller and harder ball than softball, hence the term SOFTball.