The GPS is not under the control of the civil aviation authorities, which may make them nervous about trusting it - especially when the entity in charge of the GPS has declared the ability and intention to degrade it regionally if it suits their requirements
It should be eminently possible to mitigate this particular concern by using pseudolites local to the airspace, in fact I feel confident that were that to gain momentum then it would be cheaper than installing and maintaining more traditional ILS equipment and beacons.
I'm sure the current reality though is money as others have stated, I'm less convinced of the not invented here argument, few aviation technologies would not fall into that categorization.