GaN would be a wonderful material and could even give better results - but there is a big problem with GaN: You can not buy GaN-wavers! The production is - at the moment - quite comlicated, so you will hardly find single crystals with more than 1 cm diameter.
The usual applications (e.g. blue or green LED) are using Si or better SiC as substrate, on which they are growing GaN from the gas phase (GaCl3 + NH3 -> GaN + 3 HCl). This seems to work when very thin GaN-layers are needed. For proper semi technology these films seem to be much too thin.
So at the momet and the near future I do not see competition, and if - it seems you could use a lot of the POET IP also on this substrate! I am a chemist, so I hope some semiconductor specialists can give further input!