I can support "Please don't answer if the question is obviously poorly posed" as a guideline, as long as it isn't enforced blindly as a hard and fast rule.
You say that it doesn't happen very often. I tried to find some examples with careful googling ("closed as unclear what you're asking by" OR "closed as off-topic by" OR "closed as too broad by" academia stackexchange). I couldn't find any closed questions where the same person voted to close and answered the question. (Although I have occasionally written an answer to a question that was clearly poorly posed, e.g. https://academia.stackexchange.com/a/107357/32436.)
Could you post some links to some examples that concerned you?
I'm a bit more bothered when I see a high-rep participant contributing an answer which gets wildly upvoted, and dozens of people getting involved in very involved discussions, while the answer gets closed. This suggests that we have more work to do as a community to get on the same page about when to close questions.
Also, I think it would be helpful if we put together a set of canonical questions or common questions. Benefits:
Easier for askers to find the information they need.
We'd see fewer questions that are variations on certain basic themes.
It would be easier to close repetitive questions.
We already have some questions and answers that would be candidates for such a tag (although they might need a bit of adjusting).
Some possible topics:
- How does funding work in country X
- How do I go about changing fields
- What should I do if the professor seemed agreeable to something but is not responding to email now
- How do I strengthen my application to grad school given such-and-so weak areas