This has been an interesting read, but I still don't understand fully how this is being marketed as a privacy feature. For context, I'm specifically reading the Mercury wallet statechain implementation. Yes Mercury doesn't have access to your funds as it requires a 2/2 multi-signature, and yes funds are still safe in the case of Mercury being attacked because of the timelock, but what I'm having trouble understanding from the perspective that this is meant as a privacy implementation, is that while the blockchain may not be able to reflect a correlation between the user and the funds while in the statechain, the Mercury server would have full knowledge of all owners of coins that they have to sign for right?

So it would be easier for a government backdoor to be implemented on a chainstate provider rather than a lightning network node who doesn't really know where you're routing your funds to, and the sheer number of lightning nodes that would have to be tapped is infeasable.

Please let me know what I missed in my understanding of this.