Of course that pedestrians-blocking-right-turns problem is easily solved by the three-light cycle used in many busy downtowns during peak hours:
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Red light for pedestrians in all directions, and east-west auto traffic. North-south traffic has green and can make unimpeded right turns.
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Red light for pedestrians in all directions, and north-south auto traffic. East-west traffic has green and can make unimpeded right turns.
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Red light for auto traffic in all directions (no right-on-red,) green (white) light for pedestrians in all directions, including diagonal.