I was going to say "GPS predates signing", but it turns out that the first GPS launch and the invention of RSA signing were in the same year: 1978. Of course the signing technology was also considered to be subject to US export control for decades ...
Besides, signing doesn't necessarily help - the easiest way to GPS spoof is simply to re-broadcast the signals received at a nearby point at higher power, so the victim receiver thinks it's at that point.
There is recent work on doing this: https://web.stanford.edu/group/scpnt/gpslab/pubs/papers/Lo_I...