A car turning left on green is also an issue because while they should be able to see and wait for pedestrians, they're often occluded by other cars and trucks, and those left turners can be in a hurry to proceed through a gap in traffic.
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.
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.
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.
Because where I'm from, traffic lights are not allowed to be set up like that. No simultaneous green for crossing traffic flows, unless otherwise indicated (eg, an extra warning light+sign under the turn's traffic light flashing when it's green and off otherwise).
What's not simultaneous is a green turn arrow with a green ped crossing. Intersections in the US are designed so that a green arrow will mean the driver has no conflicts and can proceed.
Not everyone (both drivers and peds) understands that distinction.
Direct link: https://i.ibb.co/Hn36L27/Green-crossing.png
solid green (right turn allowed) + pedestrian green (for crossing).
car and ped both have access to ped crossing. (Car should yield to any ped in crossing.)
Also, I drew a picture before I realized that this wasn't what you were asking about. But I like the picture.
C
A
R
2
|
v
--------- --------
CAR1 ->
---------|ped -> -------
| |
| |
| |
C
A
R
2
--------- --------
C
---------| pAed -------
| R |
| 1 |
| |I can't think of many places that I drive where this isn't the case.
The pedestrian crossing lights are in sync with the traffic lights, if traffic going N/S is green then the pedestrian lights going N/S will also be green even if cars are turning E/W
While vehicles are traveling north and south, the walk sign for crossing north and south is available. But vehicles are typically allowed to turn in the same cycle, protected lefts with their own cycle are common. Some intersections have a dedicated arrow for right turns and those will signal no rights while a walk sign is on, but otherwise pedestrians and right turns conflict.
My anecdotal evidence is that everyone is looking out for themselves and people in bigger vehicles will always take advantage of that.