it doesn't prevent the author from selling 1000 copies of it

To this point directly, an author who does that creates a large supply of their work. It's certainly possible, and there may be good reason to do so. However, abundance will dictate value. It's in part the scarcity of an item that allows it to achieve a high value (if the work is in demand). There are plenty of NFTs out there that are part of a "limited collection"; I've often seen five or ten authentic copies of an item; never 1000... but somebody could choose to release that many, and if they market it properly, it could make sense to do so.

One issue I can imagine in that scenario is that a creator might try to deceive their audience by releasing the same content in various places, hoping to duplicate demand among various segments of the digital artifact appreciating population. However, in some sense that goes against a creators best interests. One would imagine that long term investment in creating a unique and reliable brand is more important to somebody serious about being successful in this work. That won't prevent one hit wonders from trying to game the system, but it doesn't seem like a problem in the larger scope of the NFT realm to me.

On this point more broadly (of being able to pass digital—unauthentic—copies around), I've come to the realization that there is a difference between owning a copy ("here, look at this on my phone!") and owning a legitimate unique digital artifact ("See, there it is right on the marketplace platform with my avatar and the proof of purchase.")

That distinction might not be important to a general audience, but I bet it is perhaps something more significant to a private collector, or a curator who can leverage that in more interesting ways (admittedly, my examples above don't illustrate the full value of having a truly unique digital item. Doesn't this create value by opening up curation of art to a wider segment of people? I'm not sure what the mechanisms would look like exactly, but a curator could presumably set themselves apart by obtaining an authentic collection of "originals"; indeed, I wonder if a collection could constitute an NFT on its own, which could then be sold as a unique item. In fact, I wonder about how physical galleries might embrace this phenomenon to create a physically and digitally integrated experience.

I suppose you could set up a curated gallery of copies, too. But the market should be able to weed out bad actors. I suppose if people decide they don't appreciate authenticity, we could see curated collections of copies of things, too. But I'm sure good ol' classic law suits will still have their place as well! = )