Apple could have put a bigger battery at any time.
Yes, it would have made the phone a bit thicker, but so what. (I know that would have been unpopular with some.)
That would have defeated the purpose of the 's' then by making the phone thicker and changing the body style. I'm sure the biggest reason why the 's' maintains the same body design is to save money as they can order two years worth of parts instead of one.