HNers' LLCs probably have their names on them, they're not anonymous. This article is talking about it not just being the name of a company being in property records, but that the actual "beneficial owner" of the company not being named in the incorporation records.
I haven't looked into the exact details as I've never bought a house but from what I can gather I'd want to wrap it in an LLC.
Also FWIW the Sean Hannity example in the article seems like a weird strawman conflating consumer protection laws with "name and shame" accountability. If it's wrong to evict someone for XYZ reason, that should be protected by the law, not by fear of being "named" as the landlord. [TBC I am no fan of Sean Hannity.]
Land registry is a necessary function of local government. But this is one of those things which was historically only available within a government office, and now can be found in a second on the internet.
Personally I would be perfectly okay if my local government required disclosure of the personal ownership of LLC property owners. But I have no idea if that's constitutional or legal under federal laws.
If you want to know where a person lived pre-internet, you looked them up in a phone book, which is substantially less privacy preserving than looking up the owner of a house.
Well, post-internet, 2FA has been leaked to advertisers.