Most people will do the right and sensible thing in these situations, unfortunately we have to legislate for the idiotic and thoughtless minority who feel that the road belongs to them and this results in a proliferation of control which impacts on everyone.
It would be nice to think that we could introduce these shared spaces, but (as well as the thoughtless minority) many people are now so used to being managed on the roads that they can't think for themselves and get very confused when called upon to make a decision, so we would need years of re-education to be able to achieve this.
It would probably sort itself out a lot quicker than you think. Assuming we need years of education isn't really taking into consideration how good humans are at generally sorting themselves out. We manage it when walking through a busy shopping centre, and nobody teaches us how to do that. We just act like humans.
The reason the current road network doesn't work well is that it's not taken into consideration that we are humans. It assumes managing traffic is just an issue of handling flow. So we've designed our roads like it were an exercise in plumbing. Roads are pipes, traffic lights are the valves and traffic is the water.
But we don't act like water, so we don't need treating like that. Left to our own devices we're more than capable of getting on with it safely. As shown by those rush hour mornings when a usually busy junction is flowing freely because the lights are out.
It wouldn't take years of education to adapt. It could be surprisingly quick. To see how quick it could happen, do an experiment. Find the most obnoxious driver you can, in the biggest Range Rover there is. The bloke that bullies other road users, pushes his way into traffic, speeds everywhere as if he owns the road, and generally drives like a dick.
Now ask him to retrieve his car that you've positioned in the middle of a busy pedestrianised shopping area at 1pm on a Saturday. See how carefully he'll drive.
We drive the way we do because our roads don't encourage cooperation. They encourage selfishness, self righteousness. People sail through green lights without the merest scan of the junction to check its safe. They just assume it is because the light says so.
Take that light away and people assume nothing. Because their safety depends on paying attention. Our current road network assumes we're all thoughtless, murderous idiots with no regard for our own safety. So it treats us like we are. And as society proves time and time again, when you treat people like idiots they act like idiots.
For 5000 years we've built our cities around humans. For the past 50 we've built them around the car. The way things are right now is wrong, a temporary and rather strange blip in the history of the built environment, and an obvious dead end. Thankfully it's quite easily reversible. The only thing standing in the way, as it does with so much potential for progress, is our general inability as a society to accept anything that deviates from that to which we've become accustomed.