The problem with your argument is, the sender knows which email address received the money, and that is bad for receiver privacy. Tor fixes this: if the receiver runs a tor hidden service, the sender does not know which node receives his message. Lightning does for money what tor does for messaging. It lets you run a "monetary hidden service" -- a lightning node hidden behind proxies -- and if you do that, no one can know where your money ends up, not even the sender. Unlike monero, which tells the sender that info for free, which has led to multiple arrests when the sender colludes with one of your adversaries.
Discussion
yes, that is indeed an advantage to transacting on a L2.
one
there are also disadvantages to using an L2
two
its not hard to churn an output to mitigate this. not unlike using a proxy on LN
three
this is a weakness of ring signatures and we've known it since before they were implemented.
it isn't news, its why moving ro FCMP has always been the plan.