Two-stage turns and simultaneous green are not mutually exclusive. You can have a two-stage turn in phase with the motor traffic light sequence, but additionally also have cyclists-only simultaneous green phases.
Problem is, if I understand correctly, the simultaneous green needs a change of law, so the council doesn't have this option.
Many junctions would be much easier to cross if cyclists were allowed to use the pedestrian green phase (some already do, but that's technically red light jumping), they dont actually need a completely separate cycling phase (which would make the whole signal cycle longer).
Could the law be changed to allow that? Of course there would be the worry that cyclists then bomb at 30mph through a junction packed with people, the UK is a bit dogmatic about cyclists-pedestrian conflicts.
Another problem with simultaneous green is what to do with cyclists who want to go straight ahead. Do they also have to wait for the simultaneous green phase (in which case you have to stop at most junctions...), or can they go on during the motor traffic greens (which, in the UK system, leads to confusion for protected lanes but is standard on the continent).
In the Hembrow example video, if I see this correctly, all cyclists have to stop first and can only go during the green scramble phase (that's what Wagenbuur doesn't like...)