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.