No, I do not think we need such a close reason.
I remember sort of recently that this question, what does this error message suggest?, received a close vote for being unclear even though the question is pretty clear and easy to answer based on the error message. (It received the close vote after Yihui answered and after the OP accepted that answer, too, if I recall correctly. Or, I at least reviewed it in the close queue after Yihui's answer was accepted; maybe the close vote was cast before that.)
Anyway, if we had such a close reason, I think it would only encourage people to cast close votes like this that aren't really justified and/or come way too quickly.
Now, what does this error message suggest? might not be the greatest question on the site, but it's certainly a reasonable question and there's no reason to close it. Moreover, there are some really good and/or really popular questions on the site that do not have MWEs, such as:
So, at a minimum, I think your suggested wording of
While your problem may have answers available, it is closed as no MWE is added to your question.
is not a good idea.
It would suggest that those good and/or popular questions should be closed since they do not have MWEs. Of course, one could reword your suggested close reason, but even with a more nuanced explanation for the close reason, I think it would most likely just invite people to abuse it, and then we would end up with a lot of questions being closed that shouldn't be closed.
I think percusee's comment is right that each situation is different, and so, in my opinion, it would be better to keep the current generic close reasons, which, at least in principle, would force people to think a little bit about why they're casting a close vote and if it is indeed justified.