Why do you put fake plants in a fish bowl?

They are still wild animals,, That's what they do in the wild for protection and to gain access to food.

It depends on the species of fish. Some are eating algae which grows on or under the rock, and some may be clearing a "nesting" area for egg laying.

Fish may move gravel for many reasons, looking for food, preparing spawning site or being stone lovers like Oscars that enjoy reorganizing the aquarium by moving rocks from place to place, in my aquarium they push the whole gravel to a corner. Blue striped cichlid dig a spawning site. With Oscars you can not have real plants and be careful to fix big peaces of rocks with silicon to the bottom to avoid harming other fish or breaking the glass if pushed by Oscars.