[widdma]

This is exactly what is already done! On Earth at least. Radio telescopes around the world observe (mostly) quasars to perform geodesy. This is the main method used to measure the Earth Orientation Parameters which is need for keeping GPS/GNSS calibrated.

With it, you can measure distances of several thousand km with a precision on the order of a few millimetres. The problem is that it's really expensive compared to GPS: at each site you need a reasonably size telescope, atomic clock, some serious storage, and a way to ship all the data to a central cluster.