You can make a cover of any shape you want that won't fall in. It depends on how much the cover overlaps the hole. Even with a round cover, you can't have zero overlap or else the cover would fall in.

Now back to the correct answer, which is because the manholes are round - that begs the question of why manholes are round. It's probably a matter of equally distributing the sideways forces from the dirt plus a matter of being able to manufacture round tubes more easily than, say, square tubes or hexagonal tubes.