In an LPV approach, the WAAS GPS (not the barometric altimeter) is used to generate the vertical guidance. But the decision altitude for going missed is determined using barometric altimeter. Why isn't the DA using WAAS GPS for consistency? This way the DA will be the exact same point on the glide slope no matter what the field temperature is.
I'm pretty sure it's an artifact of the conservatism applied to the certification of WAAS LPV approaches. From a certification standpoint, the assumed vertical precision of GPS is not considered adequate compared to baro alt, even if technically it is.
With smartphones having GPS antennas that can resolve position down to inches, you could probably fly an LPV approach using an app on your phone (if someone made one) with more precision than a TSO'd aviation system, but the phone isn't certified.
It takes a long time for change to work its way through the system, and the technology tends to run quite a bit ahead of its application in aviation.
One thing never to forget in aviation is redundancy - if possible never trust a single system - better have two or even more independent sources to crosscheck their data. Such as verifying the correct GPS height with the barometer to be really sure you are not too close to the ground.