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>you'd need tens of thousands of them per city

I was thinking more find a tall building and throw a single one there. Or maybe tallest 3.

As I understand it even a small number of extra satellites with line of sight can improve results a fair bit.

So aiming at low hanging fruit rather than blanket city

>very accurate atomic clock.

Indeed, but I'd think managing that on ground is easier than in space.

What happens when the building sways multiple feet in the wind? We don't normally think about them moving, but for accurate positioning I'd think the additional distance to the beacon could be a problem.

https://en.wikipedia.org/wiki/Eurobalise Cool.

no, you arn't understanding. Those beacons would just be fixed places that know what their position is according to the GPS network.

You're tihnking of someone tkaing a GPS sattilite and putting it somewhere.