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"Let’s examine why we have RTOR in the first place and what might occur if we were to actually consider abolishing it. For starters, RTOR was instituted as a way of decreasing emissions, decreasing fuel consumption, and decreasing overall travel time (a measure of roadway network effectiveness).

RTOR is based on the theory that if vehicles merely stop on a red signal before making a right turn, except where prohibited by law or by specific circumstances – a pedestrian crossing the street, for instance – then those vehicle that are stopped for only a few seconds while they assure themselves that it is safe to enter the intersection and complete the turn, will contribute fewer exhaust gases to the atmosphere, will achieve better overall fuel mileage and will have shorter overall trip travel times. These goals were, in fact, built into the federal legislation that powers most of our traffic laws nationwide."

What I have read before is that the Eastern States adopted it to save fuel by which time the Western states had long had the rule, long before the oil crisis.
In most countries and areas, all road users must wait for a green when the traffic light is red. For example, consider the UK, which has fewer traffic lights and more roundabouts. Throughout the EU, no left or right turns are permitted on red light with a few exceptions, in Ireland and France, it is permitted if an amber arrow is flashing, rather than stopping before you turn, you slow down and prepare to give way. In Germany, a right turn on red (after stopping, just like in North America) is permitted if there is a fixed green arrow next to the red light.
In the Australian state of New South Wales (and the the Northern Territory), a left turn on red (we drive on the left) is permitted only where a sign permits it. Otherwise, red means wait for a green throughout Australia and New Zealand.