Just breaking this off from T6797:
Do you have a more specific idea in mind?
I currently think of user stories as kind of a crutch for users who aren't sure how to write a report (notably, they force you to describe your problem instead of your desired solution), but I don't feel like they're inherently helpful if you're good at describing and contextualizing a request. Is this roughly the angle you're coming from too, or do you see more value to them beyond just being a template for writing an effective request?
One thing we could do is just build a dedicated "request a feature" form, which could have a more tailored (user-story-esque) template and less confusing stuff (e.g., no projects field for users to type "Phabricator" into). Under the hood, this would just file a normal task. But they might help in getting users to report problems rather than request solutions. (I think this is also more of an issue with feature requests than bug reports, although we could try the same thing for bug reports.)
Does that sound like something that might be worth pursuing? I think it could be totally custom and not part of the upstream, so the pages could be specifically tailored to whatever we're after.