Thanks for the explanation. It might be that your KYC source doesn't support L2s now but in the high fee environment that might change very quickly. Binance has added LN at the previous fee peak.
With LNs coinjoins aren't needed and don't even make sense. In Liquid they're possible but given that the amounts are blinded by default there's less need to do it.
I'm not saying that L2s magically fix all the problems,. They don't and they especially can't help you with utxos in L1 cold storage. But some problems that they don't fix, like the KYC source problem, may be better ascribed to lazy exchanges or tyrannical govenrments.