GPS altitude does work if used in the correct circumstances. For something like £20,000 you can buy a "GPWS" system for GA which consists entirely of a GPS and a contour database of the region. There is no radar altimeter. I've seen a demo of it.
The GPS altitude is compared with the terrain map and it takes into account your flight path, warning you if you are going to hit something. It's a certified system which you can buy today from Honeywell and probably others.
Personally I would go for a radar altimeter, at about 1/3 of the price. That would be actually useful as a final safeguard on instrument approaches.
I am sure that if aviation was invented today, a lot of things would be done differently....