The question, though is why would the Doctor regenerate into someone who talks with an American accent? Yes, the Doctor's voice and accent changes with regeneration, most notable with Eccleston's Northern accent or McCoy's or Capaldi's Scottish accents. But most, if not all Time Lords speak with a British accent. The only exception that comes to mind is the Eric Roberts Master, and that can be explained as the Master just adopting the speech and accent of his current host body. Given that Gallifrey is essentially Space Britain, a non-British Doctor speaking with a foreign accent is really going to stand out indeed.