They have value because people agree they have value. Trusted third parties (like courts) help people come to that agreement, by providing transparent, objective processes to settle legitimacy and ownership disputes (in the happy case, in the not-happy case they use physical force to reach agreement).
Personally I don't understand the controversy, blockchains are a different kind of trusted third party that also help people come to agreements, by also providing "transparent, objective processes to settle legitimacy and ownership disputes". These third parties aren't mutually exclusive, and the role of blockchains/NFTs aren't fundamentally different, they just use novel means to help people come to agreements, within the same social constructs we've always had.
The problem with using NFTs to verify ownership is that they actually make it much harder to resolve any disputes. An NFT can't be transferred or modified without explicit permission from the owner of the NFT, which means that any dispute is impossible to resolve without bypassing the NFTs entirely.
For example, let's say you have an NFT that represents something tangible (and not just some link to an image download). What happens if the owner of the NFT dies without setting up a way to transfer their NTSs? What if multiple, seemingly valid NFTs point to the same object? What if the NFT was never truly valid in the first place? What if an NFT is stolen?
In all of these situations, a third party (like a court) would have no actual power to fix anything within the NFT space. A hard fork is theoretically possible, but that becomes impractical to do every time someone has an NFT dispute. The only option is to just declare an NFT invalid. But if you have some third party that controls the validity of NFTs, then you might as well cut out the NFTs and just rely on the third party.
I think you're misunderstanding my stance here, I'm not arguing that NFTs are always better than other trusted third parties. I don't know enough about their details to make a claim like that.
In the terms of what you're saying, I'm arguing that the space of scenarios in which people can't come to an agreement is different for NFTs vs. legal systems, because NFTs provide some self-service mechanisms for proving ownership and legitimacy. I'm sure those come with tradeoffs, as you've mentioned. I'm not in a position to weigh those tradeoffs yet, nor claim that one is always better than the other. I think it's too early for that.
More concretely, courts, NFTs, et al are tools for reaching agreements. There's no reason to dogmatically cling to "on-chain" if it's not helping reach an agreement, and there's no inherent reason things can't be mixed between on-chain and off-chain, just as agreements can be made in court vs. out-of-court.
Right! Which is why NFTs are specifically not representing anything physical (despite certain people within the space admittedly pushing this misguided notion). They work because the NFT itself, the ledger entry, is valuable.
Personally I don't understand the controversy, blockchains are a different kind of trusted third party that also help people come to agreements, by also providing "transparent, objective processes to settle legitimacy and ownership disputes". These third parties aren't mutually exclusive, and the role of blockchains/NFTs aren't fundamentally different, they just use novel means to help people come to agreements, within the same social constructs we've always had.