There's good reason for them to have considered these questions too, as a lot of the satellite-based positioning systems prior to GPS, such as the Navy's TRANSIT, involved both a more active receiver and offloading parts of the work to ground stations. This was very practical at the time, as is TRANSIT fixes were so complex that GE had to design a special computer with a cylindrical chassis so that it would fit through the porthole for installation in submarines. This replaced the previous situation of the submarine having to send its TRANSIT observations to a ground station for fix calculation.

You can still do this with GPS if you want. In the surveying community, it's not unusual to collect an extended period of raw GPS observations (e.g. 48 hours) and then submit them to NOAA's offline GPS computation service OPUS which will return a fix by email a while later. This can result in a more accurate fix but perhaps more importantly a more consistent fix, since OPUS will apply the exact same sophisticated solver used for other government geodetics like survey benchmarks. The tradeoff is that OPUS is slow enough that it tends to run on a queue.

In any case modern GPS involves surprisingly active receivers since smartphones commonly use AGPS over IP to accelerate receiving ephemera.