On a green arrow turn, drivers are looking to where they are going. Legally crossing pedestrians are in that cross walk where the driver is looking.
With right on red, the driver is also looking to where they are going, but legally crossing pedestrians are not there, they are directly in front of the car.
The riskiest thing for a pedestrian is approaching a right on red car from the left, because the driver is simply not looking at you.
The big problem with right on red is that it perfectly synchronizes them to hit each other.
Say a driver and pedestrian are at the same corner facing the same way and the pedestrian wants to cross into the area the driver wants to turn. The street is busy so the driver can't turn right on the red and the pedestrian isn't gonna just walk against the signal into the traffic. Cross traffic lets up, either because of a big gap or because the light has cycled to red for the cross traffic. The conditions that both parties require before making their move have just been satisfied at the same time. The pedestrian walks and the driver turns, leading to inevitable conflict. If both the driver and the pedestrian are in a hurry and trying to shoot a gap in traffic and go quickly there can be no time for either party to avoid the accident.
Edit: The above example is crosswalks only, no dedicated pedestrian signals.
> Say a driver and pedestrian are at the same corner facing the same way and the pedestrian wants to cross into the area the driver wants to turn.
That's not a thing that normally happens though. In a regular four-way intersection, if a driver is at a red light, the pedestrians that are allowed to cross are the ones that are crossing the street the car is on. If the car wants to turn right on red, then the pedestrians it has a risk of hitting don't care about the traffic that the car needs to wait for.
This seems to not actually be the case in my experience, because right-turn drivers love to look to the left while turning right, because they are afraid of a fast-moving car appearing from the left, but they think they already verified that no slow-moving peds are crossing on the right.