I believe women can and do hold high positions, and for the most part, legitimately. It's in the highest offices of government where their fallibilities should not be entertained. As the CEO of a corp. some woman can function fine, as there are always stockholders, employees, and the public to provide proper checks and balances, but as President, Vice President, house speaker, they should not. IMHO. There are exceptions of course, but generally the Bible doesn't mention it as a positive occurrence. Woman was created as a helpmate, not a head.
I've personally worked for a couple women, and their decision making was flawed, in many instances, which I know are isolated incidences, but somewhat indicative.