If everyone WOULD stop on red and LOOK before turning right, there wouldn’t be a need to go back to stopping until green.
I’ve had to slam on the brakes (in both personal vehicles and the big rig) to avoid a collision with someone turning right on red without stopping, and apparently not looking.
IMO, that wouldn't fix the problem completely. Right-turning drivers who do look to their left to ensure the lane is clear usually focus where you'd expect - the cross-traffic back at the intersection. There's now a big problem with drivers in a left-turn lane (cross street heading opposite of the right-turning car) getting a green arrow... and instead of turning left, they pull a U-turn right in front of the right-on-red traffic. I've seen three such accidents in as many weeks, one of them a very hard hit with a wheel sheared off and bouncing through traffic. It's all due to people missing turns due to smartphone distraction, then being too impatient to find a safe place to turn around.