Yeah, that would be cool.
I was thinking the other way around. Because you need to press the S button to get into that mode, I would argue more often than not you want the car loud, not quiet. And fast, not neutered.
So for me, ideal would be
regular mode = throttle and everything setup for max performance, exhaust flaps open
S mode = flaps closed, throttle calm like stock or something
That way S mode can be wife mode.