Sure, but the dealer is also a sender at some point in time and vice versa it's not like you can just be one.
If we're talking about practical attainable privacy I think that is the area where Monero shines over Lightning. Because of it's complexity most lightning users are largely using custodians so their privacy is just ok and probably worse overall than the average Monero user. Similar privacy to a traditional bank where the third party can see your balance and transactions.
I think that is largely why DNMs mostly use Monero. Because despite Lightnings potentially "higher ceiling" for better privacy for advanced users it's more difficult to use that way for the average user in practice and Monero just "works" by default and has been good enough (so far).
Yes, I know it's not perfect and has flaws like your presentation shows. Looking forward to FCMP++ to resolve or bolster some of these attacks. Great job by the way I watched this video when it first dropped and appreciate your content :)