There's also another aspect that seems nobody talk about.
If I run a LN address server on my node machine, or even on a VPS, but pointing to my private LN node... then who would pay me to my would know even more about me:
  • who register that domain, IP / location of the servers
  • LN node ID, even if is private, IP/location
So why would I reveal that information with a tip / zap? Yes, I could run a LN address server over Tor, but again, why would I want to complicate like that just for a damn zap/tip?
Running behind a custodial pseudonymous account is the best way to hide.
Exactly right. That's another part of the reason I use Alby for Nostr, it's effectively an abstraction layer.
As you point out, you could run it through Tor (my node is only accessible by Tor anyway) and in fact you can even pay for domains and VPS's with bitcoin, but that's a whole lot of hassle if you all you want is a lightning address.