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You can build GPS (well, a GNSS would be more accurate) system without atomic clocks.

One way to do so requires user equipment that can transmit back to the satellites, but that will already be the case for SpaceX's customers.

You can also use Doppler measurements to get your location, although this tends to be less accurate, especially if you're moving quickly

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An interesting use case for a "backup" GPS is to rely on GPS itself for the accuracy you need, but look at the other constellations to verify if GPS is being spoofed - in that way you can protect yourself against the GPS misdirection attacks (e.g. by relaying with a carefully calculated delay) that have been performed multiple times now; you'd know that you're getting a fake GPS signal and can't rely on it.

You can also use Doppler measurements to get your location, although this tends to be less accurate, especially if you're moving quickly

There would still be a market for lower cost lower resolution location.

I wonder if the resolution would be better than cellular and/or wifi triangulation. Obviously those won't work in remote areas..

But GPS is cheap enough and widely enough deployed. Devices like laptops that don't usually have GPS are usually used indoors. I don't see the market.

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