"but it seems as intuitive"
Knowledge can come only from reasoning based upon observations. You cannot know anything by intuition. You can believe your intuitions and feel that they must be true, but you cannot know they are true.
Without actually studying the question in some detail, I don't see how one could intuitively conclude that exercise increases physical strength.
We are adapted to conserve resources so anything that requires resources to maintain will be reduced if we don't actively use it. Muscle tissue, brain cells, you name it if we don't use it it will atrophy.
There are plenty of examples, both in nature and in the human body, of "use it or lose it" and "use it up and it's gone".
It's less intuition and wisdom than many people think; gut feelings for example should be examined, though they're often telling you something important.
I think it's reasonable to infer that, as we are human bodies, we would know how to make ourselves stronger. The idea that mental exercise keeps the brain sharp comes from a similar intuition; it is not surprising to see it confirmed through study.
Sure, you could say that mental exercise keeping the brain shark comes from intuition. And I could say that it's intuitive that mental exercise depletes the brain and makes things worse. I don't see how you decide which one is right without going out and studying it.
It is not typical of our community norms to downvote reasonable arguments you disagree with. Just FYI.
Don't assume the person downvoting you is the person you're replying to.