Pressure altimeters have 3 main errors (forget the daft RAF 'PITCHBLOT' nonsense):
1. No machine is perfect, so instrument error, lag and hysterisis will affect any such altimeter to a degree.
2. Installing an altimeter in an aircraft will induce certain errors, such as position error and cockpit temperature.
3. Even if both altimeter and installation are 100% perfect (impossible), the atmosphere in which the aircraft is flying probably isn't 100% International Standard Atmosphere, to which the altimeter is calibrated.
These errors may be additive or subtractive - but they will always be there.
A good pressure altimeter is probably accurate to ±30 ft - but that also assumes that the pressure setting datum is accurate.
I don't know whether GPS altitude is measured against an estimate of local sea level with reference to the Earth's centre - 'sea level' is not the same world-wide. Or whether an assumed perfect oblate spheroid provides the GPS datum?
Whatever. GPS altitude is a useful back-up, but that is all. It could only be used as a separation standard if everyone carried GPS and used the same 'earth model'. Which, outside CAS, will never happen.
Mind you, when the OAT was +3 deg C and it was getting wet outside, I was very glad to know my GPS altitude and, assuming 2 deg/1000 ft, to be able to assess the risk of ice....
...whilst driving through the Eifel on non-winter tyres, that is!