Or that it's not by default, or that's it's not cost efficient i.e pay either more money or pay with time, or that "adding privacy" also "adds information" like taint
but in general yes bitcoin has privacy, but there's more to the picture
Discussion
Zooko also makes a similar point, its better to reveal nothing.
adding layers leaks information when you peg in and out of the layer, even if transacting across the layer is totally private.
in both LN and Zcash
technical best practices could provide great privacy, but usability and adoption issues mean technical best practices are rarely the condition the user operates in.
the best case for practical LN privacy right now is that the barrier to running a node is dropping.
NOT this bullshit about "theres no proof you paid a pubkey"
if nodes are ephemeral and channel management isnt a headache, users can periodically move funds to different dead-end nodes. just burn the pubkey.
so if we have that
and new Monero users know about poisoned outputs until FCMP is done...
those are our tools for the next 5 years.