Technology

Nothing to prevent it except money. The issue with PNT satellites around Mars is how many satellites would have to be sent (smaller planet and less accuracy needed, so maybe we could get away with 12 instead of 24), plus the ground command and control stations plus monitoring stations. The ground part is probably the most critical piece of why GPS is so accurate, and I'm not sure we could do that from Earth. Definitely couldn't do the monitoring from Earth.

We'd have to be able to build an accurate ephemeris table for the Mars satellites, have accurate clock updates, monitor the signals being transmitted to do updates, etc. While we could do the commanding and controlling from Earth, I don't know if we could do the things from Earth that make GPS accurate. So not only would we have to send 12 satellites to Mars, we'd have to build monitoring stations on Mars to do the ground portion. Technically doable, just not financially feasible when we have star trackers and other navigation systems that work well enough for now.

I work on GPS satellites and am on the team working to define the next generation of GPS satellites. The beacon idea you are talking about is a terrestrial augmentation system. We have that here on Earth already, and it's critical infrastructure. On the moon, you could add nodes that receive GPS time and are used as a navigation aid on the moon. I doubt we would spend the money to put a GPS satellite at a Lagrange point anytime soon, since the benefits would be minimal for a single satellite. There is a lot more military interest in cis-lunar missions, though, so there might be benefits later. Repeater nodes on the moon's surface might be worth it, if we start doing more missions there.

Lagrange points are also pretty far away (the closest one is 1 million miles away, while the moon is 238,000 miles away. Current GPS satellites barely have the power to send a usable signal to the moon. To get a usable signal from Lagrange distances, the power would have to be much much higher (power drops as a square of distance. There's also the issue of building a satellite that lasts long enough in that radiation environment to make it worth it, since launching a satellite that big that far away is expensive. And that still would only help on the way to Mars, since Mars is another 99 million more miles past that (extremely rough numbers, since the average is 140 million miles from Earth but closest is 34 million miles and I have no idea what the distances would be to L4/L5 points).

Ah shit, I scheduled a dentist appointment for that day.