You also need to know where the satellites are meant to be at any one time. That means a stable orbit. Starlink isn't really designed for that.

It then also needs to be signed/secure so that its not spoofed.

Then your signal that your measuring time from needs to be transmitted often enough and robust enough. Plus your time source on the transmitter needs to be accurate enough.

It might be possible with starlink, but you'd also have to trust musk....