What you're saying is true. The only problem is, because of it's complexity in using it this particular way, the vast majority of Lightning users aren't using it in a way you are describing. That actually hides the receiver from the sender without simply shifting trust in their privacy to a third party (custodians, LSPs, and proxies) similar to the privacy of a traditional bank. You can look at custodial LN wallet downloads, popular larger LSPs like Acinq, Nostr LN addresses, etc for a few metrics on this.

Also, nostr:npub1lxzaxzge0jq9u9cecucctdt5lslwgp7hcxmp2l0wn8r2ecjenwasu6svxa always brings up a good point imo that LN network privacy guarantees aren't quantifiable to the public (but is to larger custodians and nodes - nice centralizing honeypots for malicious operators, criminals, and state actors who potentially have insight to a vast swath of the network) while Monero privacy guarantees are quantifiable.

TLDR Room for improvement for the default privacy of both.