There was a recent change to the close reasons, and I think the newly crafted one fits perfectly here in a few ways.
If the question was old and there is no way to tell what the original cause was then
"This question was caused by a problem that can't be reproduced"
fits that aspect. Moreover, it would also fall into the clause
"this one was solved in a manner unlikely to help future readers"
as the answer cannot really be confirmed. Mostly though, the last line of the close reason points out to the user that they should really include some sort of demo or reproducible issue.
"This can often be avoided by identifying and closely inspecting the shortest program necessary to reproduce the problem before posting."
I would suggest using this close reason for older questions. Off topic -> "This question was caused by a problem that can't be reproduced..."
For newer questions however, I don't think it would fit as well. Often these questions will overlap with other close reasons. If there is a link to a website, but no actual code is included, then that question is unclear or too broad. It would really benefit from having the problem code included in the question. Without it, users could speculate that all sorts of changes would need to be implemented. So too broad could fit
"There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs."
Unclear could also fit here, especially if the title is, "debug my website" (which would really benefit from some extra clarity). I think this might fit newer questions a little more accurately as the problem still exists, and if it were to be highlighted then perhaps it could be properly addressed.
"Please clarify your specific problem or add additional details to highlight exactly what you need..."
In the end, these types of questions definitely need to be closed. Choosing a close reason is important, but so is maintaining high quality content.