I don't buy your assessment that an untraceable UTXO is *required* on your ln channels for complete anonymity, though it certainly does improve it. Omce you open a channel, the only public information available is who you opened a channel with, not who you transacted with. One does not need to be a sysadmin to run a private ln node, there are packaged solutions available. Agreed the tools can be improved to increase privacy in a straightforward way.
Discussion
I'm talking about getting to the level of privacy that Monero provides by default. Yes having a nonKYC UTXO is vital for having no link of your channel activity to your identity from you channel peer.
You need to look into timing analysis and BGP vulnerabilities in the Tor protocol. Lightning hops are vulnerable to the same attack vectors and the more metadata you give, the more trivial the deanonymization.
Yes, I understand these vulnerabilities of tor and the lightning network. The meaning of "privacy" is a matter of degree, not a binary quantity.
> You need to look into timing analysis and BGP vulnerabilities in the Tor protocol
While looking at that, also look at how those vulnerabilities apply to monero's Dandelion protocol: https://arxiv.org/abs/2201.11860
Key quote: "our analysis of Dandelion and Dandelion++ indicates that they do not offer high anonymity either…an adversary that controls 20% of the nodes…[can] intercept [enough] transactions [to where] the median entropy is about five bits…equivalent to 32 possible originators per transaction."
You can stack dandelion++ with Tor or i2p. Plus Monero has both on chain AND network level privacy. If dandelion++ is broken all that is proven is that your IP did A transaction. Not what the transaction consisted of since reciever and amounts are still blinded.
With lightning, the privacy is entirely reliant on the obfuscation of the chain of hops. If origin and desination are linked the whole transaction is revealed and linked to you.