I am (perhaps naively) wondering whether a blockchain can be sharded hierarchically instead.

Each shard works like a channel like in the Lightning Network and the channel can have sub-channels, this means the channels all have their own blockchain, i. e. they are blockchain shards. To verify a transaction from A to B it's like a tree walk from a tree node A to the other tree node B. First verify the channel A is in, then go to the parent channel till the common parent channel is reached then descend again to the partner B's channel, verifying on each step ascending and descending.