My concern is that important details may hide under the notion of “privately”. A “private L2” can indeed provide strong cryptographic guarantees, but in practice a user would need to trust some centralized infrastructure to make use of those guarantees. My intuition is that “offchainness” improves not only efficiency but also privacy by virture of having zero on-chain trace for most interactions. I admit that this is a bit hand-wavey; we need to think more carefully about exactly what offchainness gives us.
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