What blockchains provide is transaction ordering as a service. If Y is an NFT, what prevents that from happening is the code on the blockchain: the same kind of code (literally, on Ethereum) that prevents Y from being a fungible token for a cryptocurrency that they send to two people (aka "double spend").
If Y is not an NFT, but you know the original owner X, and you wish to create an NFT, the same kind of mechanisms work: the first time you attempt to assign ownership is the canonical one. Which you seemed to get up-thread, you just failed to "do the math" to see why digital signatures alone don't support that as you are so sure cryptocurrencies have no value.
If you send two digital signatures to two people claiming they both own something, the big issue is that the second person might not even know the first person exists. You need some kind of mechanism to invalidate the second one by exposing the first one in a trustless global ledger of events.... that's what blockchains provide.
If you only care about the semantics of disputes--which is potentially fair for claims over a physical object: it acts as a kind of "second factor"--you get a long way by just including the entire chain back to the root whenever you transfer ownership, allowing people to show prominence over other chains they obviously dominate...
...but any time there is a conflict--and not just on the original sale!--in your histories you can't compare timestamps to resolve the dispute as you can't trust them: digital signatures cannot show that one thing happened before the other thing as any timestamp is just data being signed, attached by the signer, and is meaningless.
To resolve these conflicts you need to use your distributed ledger to establish that no such signature has been signed previously: you need a way to authoritatively assign prominence. If you have a solution for this, what you have invented is a cryptocurrency and could be used as such (as there is no relevant difference between fungible and non-fungible tokens).
(And note that this is true even if you try to solve this by using some complex web-of trust of a ton of random third-parties or overlapping sets of parties that different people haphazardly might choose to trust instead of a linear blockchain... you are just talking about systems like Holochain or Stellar or Avalanche instead of systems like Bitcoin or Ethereum.)