It's just a note with a URL to a video, right? But I guess it could be made as its own separate kind.
Discussion
Whole benefit of a story is its a temporary thing that disappears after 24hrs. Would it be possible to have a note event that all relays agree to delete in 24hrs?
Not really. You can try it, but you do not have any enforcement mechanism. It would have to rely on trust with its key feature. That's a big no no in my eyes.
Have it be a link to a video, the server serving the video can delete it and then the link won't work and the note expires so people don't see notes with dead links.
If you have an wnforcement mechanism to delete the video, sure, why not. I'd say however. that that is a solution in search of a problem.
Not really. Permanent stories are fine.
It wouldn’t necessarily have to be the relays that respect it. You could have a NIP that provides an “expiration date” and clients that support that NIP would know when to stop showing that story.
Expiration date of events is already defined in NIP-40:
https://github.com/nostr-protocol/nips/blob/master/40.md
No need to define it, just to code clients and relays supporting it.
Nos.social supports disappearing notes. You can even choose between 15 min, 1 hour, 1 day and 7 days in which the note will disappear.

Does it delete after some hours?
As long as it's not the IG model of "stories" which is about pushing content down your throat as fast as possible... it could be very powerful for those who produce value from videos as opposed to text or graphics.