Agree that it only loses bandwidth efficiency; that said, you could also make a simpler bandwidth savings scheme, that I described as “shadow chains” a few years ago here: publish the block data to the chain, and only verify them on chain if someone complains within some time window. Thinking of it as a privacy scheme is interesting, though I imagine I could probably come up with some parametrization that shows that the privacy usecase of your scheme is basically a more complicated version of coinjoin.
That said, perhaps we should think much more seriously about cryptoeconomic tumblers, now that we’re clear that that’s the goal; with security deposits it could be possible to design one that’s quite powerful…