Since a blue is a harsher penalty than a yellow, then if a ref is thinking that a player already on a yellow might deserve a blue, that should be a bit of an indicator to them that they've already gone past the requirement for deserving a yellow, so they should be sent off.
It is definitely worth taking a yellow to stop a dangerous attack, and teams like City take it in turns to 'professionally' foul the opposition. They're also not at much risk of a yellow for other reasons. Them being taken off the pitch for 10 minutes would be a good deterrent .