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Pools are not nearly as distributed, and the liquidity in them is largely whale recycling... and probably sybil'd as these things have a record of.
The overall amount in channels doesn't matter, because you're not leaving or entering one. You're passing through, the swap(s) out are just regular chain tx's.
It'd be moronic to send KYC exhange coin directly to join pool, that action alone gets extra scrutiny.
How many times do people have to get burned before everyone agrees these are stupid ideas? OXT and zkSNACKS have been the source of some of the biggest drama ever in Bitcoin because the very concept is fundamentally broken.
See other posts about the paradox of privacy:
#1221581
#1018656
#1253207
#1496777
Having an LSP opening a channel to you, withdrawing to lightning, then swapping out to cold storage leaves nothing to analyze assuming you don't yolo one-shot the same amount or recombine them later. (See links above how privacy is ultimately always a practice, and all privacy tools do is harm because they feed a lazy rube an excuse to not learn good practices)
Option B
Lightning is the largest Coinjoin