Yes, you can do swap, with the problems I quoted above.

It is as private because of two things:

- you can have as much privacy as you want and you can want same privacy as Monero. No public record of transaction anywhere. And that is regardless of sending and receiving counterparty's choices

- you can actually use it in many more cases, making your financial life more private. I remember at one point a Monero meetup where people were sitting at the bar without drinks. I came to ask if they're ok and they reluctantly said they can't buy drinks because the bar only accepts Bitcoin. So I got them drinks. Many Monero maxis would not do a swap (not very private even, the provider sees the details of the tx, even though they can't identify either party), and especially online, the choice is Monero or credit card. If Monero is not accepted, they pay with credit card. My choice of practical private online transaction is just bigger. I'm not a Bitcoin maxi, I'd gladly pay in Monero and I actually like to do it, but I simply don't have the chance that much. The shop I use most for online purchases (Alza) takes lightning, shitcoins like usdt, but no xmr. I can do swap, but I pay additional fees, I have to wait and hope the swap goes through before the invoice expires (not lightning invoice, just the general payment code expiration due to exchange rate). So for my practical purchases, Lightning is just so widely accepted that it does not make any sense for me to look for other merchants that accept xmr. There's no sender information in lightning transaction, so I just pay and it's private and instant.

So practically, lightning is what gives me financial privacy. Monero is just too niche to work in practice.

BTW: for swaps, I started using Zcash, thanks for your howto, it works pretty well.

I've also done the anypay.today project for this. You scan a QR code, it gets converted through trocador, the source is always lightning because I don't want to wait for miners in order for the payment to go through. One click, instant confirmation and whatever shitcoin the recipient wants they get. With Monero swaps, it's often 10 or more minutes until the recipient sees the tx.