You're not even buying the "1s and 0s" with an NFT either. You're buying a record in a proprietary (albeit public) database that says you "own" it. There can be many records in many propriety databases claiming the same thing and none has any more legitimacy than any other technically speaking
Why the quotes on "own"? You can hold it, trade it, or destroy it—curious what other factors you see as necessary for "full" ownership of a digital token?
Legally speaking, the Land Registry (in my country) is the arbiter of whether or not I own my house. Because of, like, the law. There is no corresponding law that says owning an NFT means I own [any rights to] an artwork.
You can't duplicate or send your house by email. The "art" linked to the NFT can be duplicated bit-for-bit. What is unique is the NFT, that is, the certificate of ownership.
Ownership is legal right, so to own a digital token you would need some kind of title to the token. Without a title you don't really own it, just like you don't own a house without the proper paperwork that says you own it.
Even with a title or other legal means of asserting ownership, in the end with digital tokens you're still dependent on their network continuing to exist.
If a national highway system goes down, your house is still there.
If a digital token network goes down, be it a token-based centralized SaaS company with an API or token-based decentralized blockchain, goes down, your assets go down with it, regardless of legal abstractions.
NFTs aren't digital media, they're digital tokens.
You own the token as you own an API key for a service, except since decentralized there's no network operator who can revoke your key ("suspend your account") as with, say, centralized SaaS REST APIs.
You're not buying the JPEG, you're buying an API key that happens to be linked to the JPEG.