One can be a level headed person and can be completely outrageous when coming up with ideas. I think both of them are not interwined, but it could be if you think it is, like a paradox.
One immediate example that springs to my mind is Albert Einstein. You could say that his ideas are outrageous that space and time are same and they are bent etc. Even people (like the Nazis) publicly called it outrageous and blasphemy. But if you think about his ideas, he clearly followed through with a rigourous mathematical proof which I think might be indicative of height of level headedness. In fact, if you skim through his process of explaining relativity to general public through his book [0], you cannot distinguish when he is being level headed and when he suddenly jumps into a bizarre thought experiment.
One immediate example that springs to my mind is Albert Einstein. You could say that his ideas are outrageous that space and time are same and they are bent etc. Even people (like the Nazis) publicly called it outrageous and blasphemy. But if you think about his ideas, he clearly followed through with a rigourous mathematical proof which I think might be indicative of height of level headedness. In fact, if you skim through his process of explaining relativity to general public through his book [0], you cannot distinguish when he is being level headed and when he suddenly jumps into a bizarre thought experiment.
[0] - https://archive.org/details/cu31924011804774/page/n10