Why would you need buses?
If all of those people switch to cars, you end up with it taking an hour to travel 1 mile by car.
It's almost as if they have busses for a reason.
But anyway, your statement is actually not true anywhere in the US except NYC. Even in Chicago, removing ALL the local transit and switching to 6-seater minivans will eliminate all the traffic issues.
Large stadium arenas are a special case, but they don't create sustained traffic, and their usage periods typically do not overlap with the regular rush hour.
If you remove the jobs and housing, traffic does get a lot better. But it's not much of a city without jobs and housing.