I have a theory that traffic in cities would be much reduced if we removed left have turns all together.

Although I guess in San Francisco most left turns on busy intersections are prohibited, so maybe they already solved this.

Then if you make traffic in the alternative direction go over or under then there would be no stopping ever.

At least in NYC, they don't ban left turns, but the majority of streets are one-way; and they alternate street by street (or avenue by avenue). So you often need to put together 3 rights to make the left. There are exceptions (e.g., 42nd, 34th, and 23rd are all two way streets); but not too many.

In my city, many largest streets have left turns prohibited at all minor crossings - if you're "getting off the main road" and need to be on the opposite side, then three rights is the only way to get there.