Bart's correct. To elaborate, I was part the USAF team that tested the first DoD acquired GPS receivers.
From what I remember, the GPS and common to all positioning systems, the orbital geometry was mostly limited by economic practicality. + and - 55 degrees, as stated in the first answer, covered the planet's highest population density. The higher latitudes would require a much larger constellation of satellites to keep 4 in view at all times; 3 low angle (the nearer 5 degrees above horizon the better) and 1 high angle (the nearer to overhead the better) to provide optimum Horizontal Dilution of Precision (HDOP) and Vertical Dilution of Precision (VDOP). The 5 degree above horizon is the limit the GPS signal can reliable account for atmospheric propagation delay in it's position calculations.
The software recognizes each vehicle by number and their current position based on the ephemeris table and at any given time. All that to say, the higher the latitude, the less likely you'll have favorable satellite geometry for a usable HDOP and even worse VDOP to the point that you'll have little H and no V over the poles. The physics for curing that would require polar orbits with vehicles crossing often enough to provide position fixes for a relatively small area with relatively little usage. I'm sure the aircraft serving the polar stations would disagree, but that's why they still have inertial-integrated and stellar navigation systems.
The US designed, deployed and continues to mantaine and manage the Global Positioning System as it was always intended to be a "global" system but as such would obviously be a two edged sword, so signal characteristics were added to provide US and allied forces position certainty while operating in hostile EM environments. I signed my NDA when I left the service, but the best explanation of the Anti-Jam/Anti-Spoof that I found in the clear are at https://www.novatel.com/tech-talk/velocity/velocity-2013/understanding-the-difference-between-anti-spoofing-and-anti-jamming/