With an NFT everyone has access to the exact same byte-for-byte copy of the art work, but one person gets to hold a special token saying that they have some special pseudo-ownership relation to it.

So, a more apt analogy would be Picasso donating a painting to a museum, but trying to sell you a certificate saying that you own the artwork, but you're unable to move it to your private collection or gain any additional access than the general public.

That seems like a pretty raw deal to me.

A signed print of a picasso painting would quite likely go for quite a bit, even if you could get the same print sans signature for $20 in the gift shop. Even one created post-death by family foundation etc as a limited edition probably would. Some people do value the scarcity and it being tied to the creator more, think an NFT represents that and thus pay more money. (I personally am not interested in owning NFTs, but "people spend money on scarce things I wouldn't spend money on" isn't exactly a new phenomenon)

Your argument is about digital art, and has little to do with NFTs. No one is claiming that the owner of an NFT has different access to the piece of digital art itself, of course.

Then, what is the value of the NFT? You own the rights to a hyperlink?

No, you own the NFT, which people value because the artist issued it.

Cool, if you want to pay real dollars for a digitally signed link to a web resource, go ahead.

The link is a red herring. Just like an original Picasso, the content of the thing you own is responsible for very little of its value (an excellent forgery would deliver all the aesthetic value of the original, but it would be much less valuable). The provenance of the thing is the reason it is valued. There’s really nothing new or unique about NFTs other than the technology used to implement them.