Its an active research topic called signal of opportunity navigation, and papers has been written saying this is possible, some of the uses the idea you mentioned. I used to be involved in using starlink signals for positioning and there are problems:

1. Public ephemeris from space-track (celestrak) is notoriously inaccurate after a while. Less of a problem for starlink as they give free access to high accuracy ephemeris from their onboard GPS receiver: https://starlink.com/satellite-operators

2. For proprietary signals like starlink they can change signals whenever they want without telling you and break your positioning algorithm. For example, starlink used to transmit some sort of narrowband CW wave at their frequency band, which can be received by cheap ($20 ish) RTL-SDR dongle and satellite TV antenna: https://www.rtl-sdr.com/receiving-starlink-signals-with-an-r... . Everyone speculates that its a beacon signal, research papers were written trying to exploit doppler positioning from those signals. Then the signal disappears, as its possible that they don't intentionally transmit those signal. They you can't use cheap hardware to capture the signal, you need expensive hardware that can capture the full 250 MHz bandwidth. This is not a problem if you use standardized signals where they can even intentionally add positioning signals like 5G or digital TV