I think you're leaning way too hard in the other direction. There's a balance that needs to be struck. A detail-oriented person may have an excellent understanding of where they stand today but have little thought for their trajectory, while a big picture person is the opposite.

It's rare for any individual to embody both aspects, so you usually pair these people up. For example: the strategic CEO + managerial COO. I've seen CTO/CIO combos with the same dynamic.

Just because someone resembles one more than the other does not mean the other is not just as important.