This is a service-related question, though, not a method-related question. There's no math equation that'll tell you your house is there when it used to be here.
"No, I'm `heartfelt-triple-coma` from 2003, not current. Oh, you're using a Spanish-language phone; I don't know which dataset you use."
GPS coordinates are just one possible solution, there's no reason to consider equivalent encodings of the same values as the only alternatives.
Sure, but (1) is there a good way to get an exact description of tectonic drift?, And (2) does tectonic drift account for all shifts of surface features (intuitively, it would not necessarily for features not fixed to bedrock, which accounts for a very large share of interesting-to-humans features)?
Of course, getting all software to support multiple datums might be a complicated matter, as 98% of things like online slippy maps and mobile phone geolocation APIs just use WGS84, the familiar datum used by GPS.
[1] https://en.wikipedia.org/wiki/European_Terrestrial_Reference... [2] https://en.wikipedia.org/wiki/North_American_Datum
(2) Changes on a smaller scale, e.g. due to a landslide, are probably less surprising when they cause a change in location codes. On the other hand, there might be some houses on a hill somewhere slowly sliding down, where the system doesn't work.
(I also realized that my previous comment can be read as supporting a flat earth theory, especially the part about the sphere being imaginary. I firmly believe that the earth is a bumpy ellipsoid, though.)
I would think you'd need a lot of targets near plate boundaries (where deformation is high for that reason) as well as in known regions of intraplate deformation.