In the CPH bridge solution too, you'll have to wait for the elevator to bring you upstairs, and another elevator ride to be back on the ground on the other side of the bridge.
But that surely takes less time. Elevators arrive quickly and move fast. I can't remember last time when I waited over 5 minutes for an elevator. If the cart just leaves I need to wait at least 1.5*2 minutes, plus whatever times is spent on the other side waiting for people to disembark and new people to embark.