yes. the difference is that all of these swap services and custodial wallets may log details of user activity and be used as means to identifying users but you are correct that the utxo you receive is different than the one you deposit if you go back on chain later

In regards of using LN for losing trace of your sats I wrote these 2 guides:

• if you do not have a LN node, what you can use
• if you do have 1 or 2 LN nodes, how you can do it
• or just some simple steps:

1. buy from an exchange BTC (use all fiat available, no worry, the world is not going to end), preferably from KYCnot.me
2. split the total amount in smaller parts to withdraw, if you buy a big chunk from an exchange
3. use LN-onchain swaps to convert, boltz.exchange, zigzag.io, coinos.io etc
4. send your batch from exchange to one of these swaps (or use a LN exchange) to onchain address indicated
5. have prepared a LN wallet to receive the converted sats (from onchain to LN): Blixt, SBW, BW, Breez, Electrum, Zeus, Zap etc
6. Make the swap and receive into your LN wallet / LN node.

Alternatives directly on LN, privately, fast
⚡️ RoboSats - P2P Full private Exchange over Tor, LN escrow (HODL invoice)
⚡️ https://t.me/lnp2pBot - Telegram bot buy/sell P2P through LN
⚡️ https://t.me/BitcoinVoucherBot - Azte.co Telegram Bot buy BTC on LN

Here also you have a comparison guide about all LN wallets

KYC exchange > Muun lightning wallet > Muun lightning wallet to BTC address.

Total cost to do this is usually less than $2. I’m lucky though as the exchange allows lightning withdrawals. Shout out to Bitaroo in Australia.

Yes, I came to a similar conclusion about Liquid as a mixing service, here are my notes:

A federated sidechain network with cheaper, faster and confidential transactions. The federation is controls a multisig wallet. To peg in, one can run a node and make a BTC transaction into an address owned by the multisig, with a claim script to validate the liquid tokens on the other side. To peg out one must go through one of the federation members either through an exchange or a swap service like https://sideswap.io. There didn't seem to be peg out limit on that swap service but I haven't tried it yet The conversion rate is 99.9% so you're paying a 0.1% fee.

What you describe is how fedimints / chaumian mints work.

https://fedimint.org/

it is not how current custodial wallets work today, but i would hope that all custodial wallets become chaumian mints in the future.

I agree with the sentiments about using Lightning and Liquid for this purpose. I see coin mixing services as outdated with surveillance technology catching up and believe that the Wasabi drama is the beginning of the end for all of them. The arguments I'm now seeing on Twitter in favor of coin mixing services are a mix (pun intended) of fear-mongering and personal attacks. That's always a sign of a failing enterprise.