Even if the LN will be PERMISSIONLESS, it can't possibly be PRIVATE since it relies on direct and/or long-living connections, which is, surprise-surprise, exactly where the government has a big edge by being almost
omniscient of the connections in the network. Also the channels providing liquidity are essentially middlemen - while the blockchain doesn't rely on middlemen, and doesn't use
direct connections, so it's true p2p, and private as long as it's not too expensive to use the base layer for mixing and atomic swaps.
