So the test for amplitude is aided by the fact that the signal strength received at the car increases by a factor of four if the distance is cut in half. Thus, you have a nice margin for setting your threshold.

With measuring the time, however, presuming that radio signal will travel on the order of one foot per nanosecond, you have much less of a threshold tolerance. If the unlock takes place within two feet of the car, that is two nanoseconds. If the key sits 20 feet away, that is a 20-nanosecond one-way travel. So this solution would need to be able to distinguish between a four nanosecond gap (round trip time) and a 40-nanosecond round-trip time.

Add to that the turnaround time in the car CPU which I would imagine to be some number of milliseconds, would 10 ms be reasonable?

Thus, the electronics in the car needs to distinguish between 10ms + 4 ns vs 10ms + 40ms. And given jitter in any modern CPU/memory/OS/electronics device, I would bet that the jitter totally swamps that.

(Keep in mind that this is a BOEC https://en.wikipedia.org/wiki/Back-of-the-envelope_calculati...)