To be honest, I have the natural tendency to want the actor to be American, because... well... it seems to make sense.
But, the more I really open myself up to actually thinking about it, rather than just being "set in my ways" about it, I tend to not feel there is a pressing need, so long as the actor is adept at portraying the role with justice to the character as well as to the 'American man'.
Without trying to be silly, I can't imagine simply never seeing, say, an Aztec in a film because we can't find an actor from that particular tribe.
The best case would be that the actor, regardless of nationality, is so good in the role that audiences are debating whether he is actually American or not.
"Are your girlscout cookies made with real girlscouts" - Wednesday Addams
I loathe that this will by default draw Batman comparisons, but Christian Bale, regardless of his thick native accent, was able to nail the lead in AMERICAN PSYCHO due to his ability to act like he is an American.
There is, obviously, the need for something 'extra' in a role like this, as the gravitas required to look the part, but also look like he carries the ideals of an entire nation on his shoulders - will take a lot from the actor who gets the part... regardless of nationality.
But, it can be done. And not simply by being an American actor. But, maybe from an actor who can pull off acting American. And, if they're really really good at their craft... pull of being the ideal American.