Thinking deeper, shouldn't every miner have the full block chain anyway?
They must, if only for the validation of incoming transactions. And not only miners. Everyone downloads at least all block headers, even light SPV wallets.
Satosi spent so much time & work keeping the blocks efficient, this seems out of place.
Well, no data structures and algorithms are perfect, neither are people who design them. For example, you mentioned the difficulty adjustment period of 2016 blocks before, but it's actually 2015, because of off-by-one mistake in the code, which has been left untouched to not ruin consensus, but causing the difficulty to always adjust 0.05% higher than it objectively is.
But I still feel like there might be a use case here. Maybe it's for independent validation of any block, of the hashing power spent generating it? Since you can't deduce difficulty just from the number of leading zeroes in block hash (a miner can accidentally discover a hash with many more zeroes, but it doesn't mean that that's the difficulty he was aiming for, nor does it mean that it should now have a role in difficulty calculations). Where would it be useful though?