Ian W : Ah the famous debate between GPS and baro altitude! Just like enbedded lateral off-set on FMS , those are wonderful ideas but full of hidden (good) reasons not to do it.
Heavily debated during the ICAO FANS meetings, , if my memory is correct ( long time ago !) main reason against was that WGS84 ( the GPS reference ) is a spheroidal while earth is irregular (a "potatoidal" was the name used) and therefore not suitable in some parts/areas of the world.
Another one was that , at the time , the GPS precision mode switch was still in the hands of the US military , and also in addition, many States would not accept to depend solely on it.