Yes, this has been shown to work very well in many places, as in your examples.
One aspect not addressed (perhaps an SPD is not the right place?) is buses. At the local consultation I attended, this was a common subject. Themes such as:
1. Stagecoach seems to have a very comfortable and dominant position: they should not be telling us what to do, but the other way round.
2. Routes and positioning of stops came in for a lot of criticism (for example, no direct route from Victoria Road to the railway station).
3. Current buses are too big for our roads. This is dictated by economics, but they often run mostly empty. We need more, smaller, cleaner buses.
4. If a commercial operator will not play ball, then take back control on behalf of the city. It has been done elsewhere and is legal.