Maybe think of NFT as a pointer to the head of a link list, the start of the data distribution chain. And we assign some arbitrary monetary value to that pointer, because, well, there's only 1 head of a link list.
There are people who buy originals because they truly like the work, and they appreciate and enjoy seeing the original, physical piece that you don't get with even the finest print.
You also have collectors who, in addition to the above, also buy art as an investment. Say you buy a piece at a small art show from a new artist. You pay a few thousand for it. They keep painting, and years later, are appearing in larger shows, or may have created a piece or two that generated a lot of attention. Now those early works you have from them could be worth a lot more as they're indicative of that person's earlier period. There are forums, exchanges, and shows exclusively for this sort of trading.
(Source: Married to a (digital) fantasy illustrator, attend a lot of art shows, and talk with artists and collectors. I hope to own an original or two from some of my favorite artists in the coming years. And no, it won't be an investment. =)
And that already happens.
When prestigious institutions are involved you'll be able to check their addresses and signatures too.
It is more about the transfer and hypothecation of value, which this scarcity and transparency allows.
If it doesn't catch on it doesn't catch on. Right now people are clamoring for this future.
If anyone could, at no meaningful cost, download a physically identical replica of a Jackson Pollock and have it, you can be sure the price of art would suffer quite a bit. Your ability to prove that you are the person who owns the work is meaningless if anyone can just also freely have the exact work itself.
Effectively the NFT should be a delegation of some of the IP ownership rights.