Yup.
Every intersection should have police on it until people get it into their thick heads to COOPERATE on the roads and not try to beat everyone else... maybe 1 in 20 you will win. But the other 19 times you will lose.
More fines and larger ones too. MANY cities in the world have the same traffic density as Beijing but they don't have this problem.
I place the blame squarely on all the people that buy their licences, drive like they do pretty much everything else when it comes to interactions with others (Be selfish) and generally think that every mistake of theirs should be others to pay for (back up and take the exit, cut across to make the exit, stop and think in middle of intersection.....)
I think Shanghai and ShenZhen are MUCH better than Beijing. Much better.
Statistics are not needed - just have a look at how people conduct themselves when on the road. Like little school children.