The shift is actually not that extreme in LEO (a few KHz at most).
And couldn’t the satellites mostly adjust for that, given that the relative doppler shift should be pretty constant between mobiles in the same spot beam?
Obviously it's not constant, but if it's uniform (enough) within the footprint of a single spot beam, the satellites can adjust for the global component both in their transmitter and receiver, and the mobile devices only have to compensate for (or tolerate) their local difference from that.
And couldn’t the satellites mostly adjust for that, given that the relative doppler shift should be pretty constant between mobiles in the same spot beam?