GPS gives you ground speed (the speed of the aircraft relative to the ground), which is irrelevant for flying. You need Airspeed (the speed of the Aircraft relative to the air).
Since icing can affect all IAS probes at the same time, thus nullifying cross-checking, it would make sense to have GPS crosschecking for errors implicit in rapid changes in IAS. If IAS changes unexpectedly and GPS does not then a warning could be issued re suspected icing. It's just another bit of filtering software that perhaps needs to be written.