Alphcentauri makes a good point about the approximation of the geoide (shape of the earth) that is used to calculate GPS altitude - it can be hundreds of feet out, at least that's what I've seen).
However, I would have thought that the error would be constant for the position. That means it can be removed by adding or subtracting an offset to the GPS altitude for the given approach and airport.
I note that apparently the latest experimental EFIS from MGL has the ability to construct a home built GPS approach and Dynon is under pressure to do the same.
How this new technology is going to be managed is difficult for me to understand, although the Australian regulatory response, predictably, will be blanket prohibition of having anything to do with it, which is not a good solution given human frailty. I am aware of the owner of at least one fully kitted RV's who boasted about his occasional alleged illegal IFR exploits thanks to his sophisticated EFIS and autopilot.