What would I have owned exactly? What would have ownership entitled... All very reasonable question. Mostly entirely ignored or handwaved...
And of course there's no reason why a NFT has to be used to represent ownership of some kind of digital art - there are other uses for NFTs, such as modeling transferable network permissions or resources.
Ultimately NFTs are a just a specific application of blockchain technology, to represent some kind of resource on a blockchain which could in principle be digital art. If people care about ownership of NFTs representing digital art, that's a social fact about what kinds of art there is market demand for; and whether it matters that the bytes of the digital art are on a blockchain or linked from somewhere else (where they could get taken down or bitrot) is also a social fact.
I actually agree that treating NFTs that merely contain a link to some bytes elsewhere that worked at one point in time is a pretty dumb thing to care about, or have a market for (and the use cases for NFTs where the bytes are actually on-chain are, at best, fairly limited, although I wouldn't say completely nonexistent). And certainly the NFT market of 2021 or so, which had a lot of such NFTs, was driven by a weird social mania and people attempting to grift upon that social mania. This has never bothered me though, because I feel the same way about many markets for physical pieces of art; and ultimately it needs to be possible for people to create markets for things I personally think are dumb or at least don't care about.
There is a difference between markets for things I don't care about and markets for things I do care a lot about, just not in a positive way. I don't think it's necessary to allow an open market exchange for phone scammers, for example, and it has nothing to do with how uninterested I am in buying people's information. Not all NFT had to fall towards that kind of thing, it's just there was so little practical usage actually being done that 99% of it ended up being that way.