[gpm]

Are those actually necessary?

Not an expert, but the whole network is on communication (with perfect understanding of the satellites locations no less), shouldn't they be able to run an ntpd like protocol to stay in sync, and just sync ground clocks to "starling consensus time" instead of "real time".

[cryptoz]

There is a pretty decent description of the problem here: https://physicscentral.com/explore/writers/will.cfm

I'm also not an expert so I don't know if you can solve it with syncing. Maybe you can. But that doesn't sound like a "just" concept to me - any solution to this is going to be complicated.