canine: Please realize that all drivers are pedestrians as well. Once you park your car, you end up walking to your destination.
Now, what percentage of pedestrians, in NY, wait for a walking signal? Once you’ve solved the problem of cars being held up by pedestrians, who are violating the law.. L&D etc, then you can go about solving the problem of turning. Its circular.
If you notice, in NYC and other very populous locales, the other light does not turn green with the first turning red. There is a 2-3 second wait time where both lights are red. In less populous areas, when one turns red, the other turns green. Think about why it is that way.