I live in the UK, and most US law is based upon English common law, it's not some immutable code given to us from above. It's based upon assumptions and capabilities of the entities participating in the system at the time the law was codified. It can and should change to make more sense if those assumptions and capabilities shift massively.
If they have only the rights that their human creators have, then access to them cannot be sold, in the exact same way that I cannot sell you a database that I have collected filled with copyrighted material. The "humans do training too" argument only holds if you imbue LLMs with similar rights to humans.
I am allowed to sell myself (in a very limited capacity) to others for them to exploit my training, even if that training was on protected material, which is a privilege humans should have, but machines should not.
However, because it is an issue with (at least historical) goals of copyright law, the common pattern that is evolving is that AI is not granted copyright of any work it generates, making it a bit of poison pill for some of the egregious ideas of corporate abuse. Not sure if the weights will be considered copyrightable either.
The UK works under the "sweat of the brow" doctrine for copyright. https://en.wikipedia.org/wiki/Sweat_of_the_brow
Under a "sweat of the brow" doctrine, the creator of a work, even if it is completely unoriginal, is entitled to have that effort and expense protected; no one else may use such a work without permission, but must instead recreate the work by independent research or effort. The classic example is a telephone directory. In a "sweat of the brow" jurisdiction, such a directory may not be copied, but instead a competitor must independently collect the information to issue a competing directory. The same rule generally applies to databases and lists of facts.
The inclusion of "human" is important there. https://copyright.gov/comp3/chap300/ch300-copyrightable-auth... - the human authorship is mentioned several times.
306 The Human Authorship Requirement
The U.S. Copyright Office will register an original work of authorship, provided that the work was created by a human being. The copyright law only protects “the fruits of intellectual labor” that “are founded in the creative powers of the mind.” Trade-Mark Cases, 100 U.S. 82, 94 (1879). Because copyright law is limited to “original intellectual conceptions of the author,” the Office will refuse to register a claim if it determines that a human being did not create the work. Burrow-Giles Lithographic Co. v. Sarony, 111 U.S. 53, 58 (1884). For representative examples of works that do not satisfy this requirement, see Section 313.2 below.
313.2 Works That Lack Human Authorship
As discussed in Section 306, the Copyright Act protects “original works of authorship.” 17 U.S.C. § 102(a) (emphasis added). To qualify as a work of “authorship” a work must be created by a human being. See Burrow-Giles Lithographic Co., 111 U.S. at 58. Works that do not satisfy this requirement are not copyrightable.
...
Similarly, the Office will not register works produced by a machine or mere mechanical process that operates randomly or automatically without any creative input or intervention from a human author. The crucial question is “whether the ‘work’ is basically one of human authorship, with the computer [or other device] merely being an assisting instrument, or whether the traditional elements of authorship in the work (literary, artistic, or musical expression or elements of selection, arrangement, etc.) were actually conceived and executed not by man but by a machine.”
The prompts may be copyrightable... but the output if you don't go in and fix it up and provide that minimal amount of human originality to it? That appears to still be an open question of law in the United States.