You're right
Cohen suggests that mobile habitats must have robust radiation shielding for them to be practical. "Radiation protection remains a challenge and a potential showstopper, as it does for all lunar base and rover concepts," Cohen said. However, there are potential shielding concepts that may well be reasonable, according to Cohen.
Radiation isn't a showstopper or even that great a challenge for an underground lunar base. Regolith is ideal shielding.
I think we need both a fixed base AND a mobile one.
Do you know anything about the cutting edge technology on radiation shielding? How good is it getting?