I am not sure how that is going to work. I assume you are talking about lightning, liquid or a similar protocol. You are still going to need to make an on-chain transaction to join that second-layer mixing protocol and a second transaction to get back full control of your coins and record the changes on the blockchain. Unless you mix regularly, you aren't going to have open channels and routes to whatever nodes you need to connect to perform your off-chain mixing. People who don't mix on a regular basis won't save anything if they don't maintain their LN channels.
You're right, off-chain mixing doesn't make much sense in a world where it is still possible for a single individual to make economically viable transactions on a base layer, without having to rely on a pool of co-signers and fee share payers. Mixing through Lightning Network and similar solutions is no different conceptually from CoinSwap but leaves even more traces in the blockchain. You exchange two unrelated UTXOs or transaction histories, but some of your off-chain activity may reveal the real purpose of the transaction and give an observer additional information about transaction participants. The more tools a user employs to facilitate a private transaction, the greater the chance of messing up things and lowering the anonymity set. This is why I support this new Whirlpool feature: your behavior doesn't change, whereas your anonymity increases, and you get additional privacy for free.