This sounds like a major liability, GPS is an extremely brittle and vulnerable system--you'd only need one or a small handful of nuclear warheads detonated in space to knock it out completely.
https://www.scientificamerican.com/article/what-happens-if-a...
OTOH it would be so much easier now to develop a celestial navigation system that works optically than it was back in the 1950s.
EDIT: Destroying GPS completely with nukes lobbed into space isn't the only way to mess it up either, it's susceptible to more terrestrial electronic countermeasures as well. It's generally not a good idea to depend on GPS alone, you need other backups as well. Pilots know this It's why they fly with a paper chart and a compass as well as GPS.
EDIT: Also, if my opening move is nuking space, I don't just deny you GPS, I also deny you all your other space-based advantages. I'd guess that would be one of the very first things any nuclear adversary of the US would do, because the damage is so asymmetric.