Question
I have a bradford pear that has babies trees growing from it's root system, why and is it bad for the tree?

Answer
Bradford pear do have roots that will come close to or at the surface of the ground. And the roots do tend to sprout "suckers" when they are exposed. The exposed roots can be covered with not more than 3 inches of soil. For a lawn sand works  good and also helps the grass. The grass will grow quickly through the sand.
Chopping out the roots will damage the tree and cause it to loose some of its foliage. It is not a good idea. The sprouts cam be cut off as they appear. They can not be eliminated permanently but will be less if the exposed roots are covered.