I agree with your analysis, but I'm going to take the opposite view because of one factor that you didn't consider: power outages. People want to have some standby storage at their house anyway, and once they have it they may as well use it to keep rates down.
(I think the real answer is somewhere in the middle, but disagreeing is more fun)
Nobody outside of datacenters and emergency services cares for power outages if they are sufficiently rare.
An outage-ridden grid propped up with uncoordinated batteries is a recipe for staying outage-ridden forever because everybody will charge at the same time.
(I think the real answer is somewhere in the middle, but disagreeing is more fun)