Here we're talking about the privacy of the owner of the LLC, not of the LLC itself. In particular, the owner wants "what LLCs they own" to be private.
But that’s the op’s point. “Just because someone wants their browsing habits/pay amount/address/sexual preferences/etc private doesn’t mean it ought to be.”
Is just as meaningful a sentence and the contrast in tone on hn when it comes to one type of privacy technology (vpn/tor/etc) and another (shell companies) does seem more visceral than logical.
the constitution does not give you a right to a pony.
It does give you a right to privacy, defined broadly as "the right to be let alone". These include the Fourth Amendment right to be free of unwarranted search or seizure, the First Amendment right to free assembly, and the Fourteenth Amendment due process right