I actually thought really hard about Kakashi, because you're mostly right. Thing is, we may know that Kakashi's
fame initially came from his dad, but that still gives us no reason to assume that his skill came from there too. Though you do raise a point with intelligence being passed down, given that that definitely happens with the Naras as well.
Still, Naruto certainly didn't get very many braincells from his dad, and if they did they're under
very good lock and key somewhere.
