I agree, the person investigating /everything/ should be as neutral as possible - it wouldn't be whomever is appointed as Director of the FBI regardless, but even if it were, Gowdy is interested in LAW not partisan games, that inherently makes him neutral.
The FBI Director steers and decides yay or nay as to where/to what extent an investigation goes. Gowdy is interested in law, sure, but he was also outspokenly critical of Obama as well as Clinton. That makes it pretty obvious to me that he is looking at the world through a partisan prism. Gowdy talks all fair and balanced, but his actual opinions are not neutral.