Certified GKH Gardening Expert
This is a sign of healthy soil. These mushrooms are very good at breaking down organic material, very quickly. It is like composting, but much, much faster. However, it can be a signal that the soil remains too moist. Mushrooms are quite vigorous, and attempts to kill them will usually fail, since most of that mushroom lives underground. There is no telling how far that mycelium goes, either. It could extend to outside of your yard.
The only, effective, way to keep them from fruiting will be to ensure that the top several inches of soil has time to dry out, completely, between waterings. They will only come out when the soil is moist enough for them to do so.
I would keep them around, though. They are doing work that would, otherwise, get expensive if done by a gardener!