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Right but as long as GPS satellites are synchronised with each other it doesn't matter all that much how synchronised they are with anyone on the ground, the position they return will still be correct.

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Take a good hard look at the GPS interface specification. The GPS satellites aren't synchronized with each other*. They are synchronized with the ground control segment.

https://www.gps.gov/technical/icwg/IS-GPS-200K.pdf

* recent satellites have limited autonomous navigation capability as a backup.

You still end up with a bunch of messages that end up saying "at time T I was at position X" where T is off in absolute terms (which you indeed can solve by using an additional satellite to synchronize your clock) and is measure with a different rate (which you cannot solve, unless you know a leap smear is occurring, or by using yet another extra satellite and some mathematics that I don't think anyone's ever bothered working out yet).

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