I might argue that inability to unambiguously calculate an anon set is a positive - systems which don't create permanent global records of usage are ceteris paribus *more* private.
There are obviously counter arguments. But I will say that, the fact that LN is fast and cheap is the 'special sauce' that makes its particular version of privacy attractive to me. Many academic studies have already pointed out ways it can be attacked actively, it is true, so I don't claim it's even close to perfect, but it actually has 'cover traffic' in the loosest sense by being fast and cheap, and for everyday users that may end up mattering more. 

 interesting take. Thanks for writing that all out.

It seems like the jury is still out on it. 
I'm not sure how much the privacy gained is just "private because nobody is looking."

did you see this one?
https://d.nostr.build/0ua3oxgiHkycwJz8.pdf 

 No, looks interesting. Censorship resistance is pretty clearly going to be far weaker in such a system just by common sense. And btw "private because nobody is looking" is not a good summary of what I was saying there :) 

 No I understand that.
Also certainly common sense that systems that don't have this sort of quantifiable metadata can be more private.

But also, as it is right now,
maybe just private because nobody is looking.