Probably does help with privacy too, although I’m not an expert on lightning privacy. As I understand it it’s “better but not perfect”.
If you use Boltz through Tor, it is almost impossible to make a link between you and the new UTXO IMO
What I do for the few purchases I still do on CEX, is I withdraw from Kraken with Lightning (free withdrawal) to a mobile Wallet. This allow me to add a step for potential regulator who'd try to track me, and avoid a direct doxxing of my node.
Then I send funds from the mobile wallet to my own node (running behind Tor). Finally I use Tor Browser to reach Boltz of Deezy and perform a reverse submarine swap from my node. I assume the UTXO received on my cold wallet is now pretty "anonymous"
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