Well, of course, Steve in particular, would wear his "cockney hat" and his "pseudo-America" singing hat depending on what he was singing.
   But, it would have been marvelous if he had kept his English voice for everything. That would have been great!
   In a way, it's weird how this "Brits Sing American" phenomena has become acceptable to the masses.
   The Brits - as a whole don't mind, and the same with the Americans.
   Interestingly, in pre-rock days, the BBC radio would not air dance bands if their singers had an American twang!
   And, of course, famously, back in 1964, John Lennon was asked, by an American reporter, why The Beatles sang in an American accent, to which he replied, "Because it sells better".