We all know that there apparently exist many questions to which nobody knows the unequivocal answer (there may be many opinions or beliefs, but no widely accepted answer).

I ask the question, "Is an 'apparent' question legitimate (or serving any purpose) if it does not have an answer after consideration by many people for many years"?

As a simple example to show that such an apparent question can exist, consider:-

"Which raindrop was the middle one to land on my head during that downpour"?

On average, there would be a 'middle raindrop' during half the downpours that occured.
We have no hope of determining the correct answer!
We can't even detect how many raindrops fell on my head!

Is the question stupid or is it possible that, just because we can ask 'apparent' questions we PRESUME there are answers to be found?

We can waste our time in a lot of useless pursuits and questions ... and miss or avoid asking the essential questions.
Edward O. Wilson in his book "Consilience: The Unity of Knowledge" says that a right answer to a trivial question is trivial; that we have to learn to ask the right questions.

There are two things to be done in life: the necessary and the impossible.