Crossref is designed for publishing workflows. Not set up for ad hoc DOI registration. Not least because just registering a persistent identifier to redirect to an ephemeral page without arrangements for preservation and stewardship of the page doesn’t make much sense.
That’s not to say that DOIs aren’t registered for all kinds of urls. I found the likes of YouTube etc when I researched this about 10 years ago.
It really depends what you’re trying to do. Make something citable? Findable? Permalink?
Crossref isn’t the only DOI registration agency. DataCite may be more relevant, although both require membership. Part of this is the commitment to maintaining the content.
That’s not to say that DOIs aren’t registered for all kinds of urls. I found the likes of YouTube etc when I researched this about 10 years ago.