I agree the part should go to whoever is best for it, but I absolutely believe that if an American was cast as The Doctor or James Bond for that matter, Brits would go apeshit. You absolutely wouldn't hear the end of it, from the tabloids on down, if Moffat and Co. announced tomorrow that the actor was chosen and it happened to be an American. The gnashing of teeth would be epic. There are already some Bristish fans saying that DW is trying too hard to cater to the American market as it is. An American doctor with a British accent would blow their minds. The apocalypse would be nigh.
For my part, I think the actor cast should be British but if I was in charge of it, I would cast my net as far as possible. The thing about British TV and film is that the acting pool is rather small, which is why ITV and BBC dramas have the same actors over and over. There's really nothing wrong with finding an American no-name actor who can do a flawless British accent if he happens to be a better fit than these other guys.