The notion of a "better question" seems inherently relative, even using the suggested counter-question, "What do I plan on doing with an answer to this question?" If the answer "nothing," flags privileged questions, then what answer(s) would indicate more important ones? You imply that the answers to these better questions impel us to do something, but what does "doing" mean? Perhaps more specifically, what does action include (and exclude) in this context?
It's relative to your utility function (feel free to take this literally or metaphorically depending on how you feel about modeling people as having utility functions). An action is something you do to increase your expected utility.
For example, take the question "should I give to charity now or invest my money and give more to charity later?" If I had an answer to this question (which I don't; GiveWell recommends the former but Robin Hanson recommends the latter), I would change my charitable donation patterns (they don't happen very often yet, partially because of my uncertainty about the answer to this question) and maybe also write a blog post convincing others to do the same.
For a less direct example, suppose you are interested in physics and you ask yourself some interesting physics question one day. You probably aren't building a rocket or anything else that would require an answer to such a question; more likely you're just intellectually curious and think the process of finding out an answer will enrich you in some way. Intellectual curiosity is probably part of your utility function.
The notion of a "better question" seems inherently relative, even using the suggested counter-question, "What do I plan on doing with an answer to this question?" If the answer "nothing," flags privileged questions, then what answer(s) would indicate more important ones? You imply that the answers to these better questions impel us to do something, but what does "doing" mean? Perhaps more specifically, what does action include (and exclude) in this context?