Valid. Make them figure out the solution.
Before quitting, think about it carefully and weigh the pros and cons. Look at the extra pay and the benefits it brings against the extra stress and the risk of going against your moral values. Moral values are too often disregarded, but constantly going against them can lead to mental health problems by creating cognitive dissonance.
(See, I've never been anywhere near a management position, so i can be straightforward)...
As for answering any question with a question, this is very similar to the socratic method of philosophy and a millenia old technique to reach higher truths.
Perhaps don't see yourself as a manager, but see yourself as a philosopher.
@fesshole I scale the effort committed to my answer with the effort required to answer their own question.
"Have you checked the manual? No? Well, off you go then."
"I see you've made a reasonable effort to solve this before coming to me. Let's figure this out together and update the process going forward if necessary."
The biggest challenge is straddling that line between convincing your team that dumb questions are allowed and encouraging them to try self-education first.
I can only assume, but it seems to me that as a manager the OP is content with answering questions with questions. It is in "real" — outside of work — life he does not like doing it.
Professional deformation, we call it. Apparently, some behaviors are hard to compartmentalize.