The same could be said about how blocks are currently shared.

The only difference would be that instead of having 10,000 nodes with the full blockchain, you'd have 1,000 nodes for each 10% of it.
And as the network grows you'll likely have more nodes anyway, so it could be 10,000 nodes for each 10%.

But the UTXO set will require a more elaborate scheme.

I don't know. If the current growth continues, and the scaling problems are solved, perhaps a doubling each year is more likely. That works out to be about 40TB in 8 years. But of course, the scaling solution might not involve having to store the full blockchain.