Did anyone of you who runs a Lightning routing node experience someone connecting privately to you, route coins through you, then close the channel?
It didn't happen to me so I guess that only extremely large/well-connected nodes experience it.
I believe Lightning deniers foresee something that they don’t want every Bitcoin user to discover.
I am not sure why you mentioned Lightning deniers here. The above sounds to me like a use of someone's Lightning node to mix coins.
No, not as mere mixers, but a censorship-resistant method to increase Bitcoin’s anon-set, and also the ability to rest the anon-set and increase it back again if needed.
Lightning routing node operators can charge higher fees for that, and incetivize others to run their own nodes.