One of the best ways to eliminate left turns is to replace four way intersections with roundabouts. This has the advantage of working even where there isn’t a grid to facilitate the “3 right turns” strategy. For a great description of why this is so effective, see the recent freakonomics podcast: https://freakonomics.com/podcast/roundabouts/
I'm a little skeptical that it would be safer for pedestrians and bikes. Bikes need to merge with traffic already in the roundabout instead of simply going straight through an intersection, and pedestrians would need to always check for oncoming cars rather than being able to mostly rely on lights telling them when they can cross. But then most of my experience with roundabouts is with large, multilane roundabouts so…
https://commons.m.wikimedia.org/wiki/File:Alternative_dutch_...
Multi-lane intersections on major roads should just have a left-turn lane with a separate signal phase.