Seems the differences are (1) data on the “master shard” is always just a copy of data on shard; it’s used only as cache, and (2) all data accesses check the cache first, and then go to the shard if not in cache.
I think state rent would be fine this way. Cache accesses could pay towards rent, so things naturally fall out of cache if not used enough. It might even be possible to use a mechanism like 1559, to gradually adjust the rent fee and target a particular amount of storage.