That's not my experience - too many drivers that are turning right will roll through intersections, looking in the other direction to check for oncoming traffic.
Additionally impatient drivers often pull up into the crosswalk, forcing you into the intersection.
(Please don't do this, it will not get you to your destination any faster, it just creates danger and confusion. Especially for cyclists and wheelchair users.)
While this is a problem, there is also the problem of drivers not having sufficient visibility from behind the crosswalk due to parked cars or bushes or trees, forcing drivers to encroach in the crosswalk at some point.
Why do you need visibility left or right to come to a stop at a red light directly in front of you? :)
When the light changes, or you're in the right turning lane, sure you need to go over the crosswalk, but that's not what I'm talking about.
Once a driver was even gently sliding into the crosswalk, looking at their phone, while I was directly in front of them. They looked up and made eye contact with me, and I watched them realize with horror that I was there. (I was fine)
In the US, you can usually make a right turn on red light if there are no oncoming vehicles.
So you stop at the stop bar, before the crosswalk. No one is walking in cross walk, so you inch into crosswalk to see if there are cars, and then you might see a line of cars, and by the time they are gone, someone might want to walk across in the crosswalk, but your car is in it.
Obviously, one can simply not turn right on red, but that is not how most people drive.
This problem is actually unavoidable at intersections with stop signs on one road but not the other road, which is where I encounter it most. There, drivers have no choice but to encroach into crosswalk to see.
Highlighting some parts of my previous comment you may have missed:
> When the light changes, or you're in the right turning lane, sure you need to go over the crosswalk, but that's not what I'm talking about.
I routinely are drivers going straight or left pull into the crosswalk. It may be more visible/memorable to me because I do a lot of walking, so they're often in my way. I don't know your situation, but if you're mostly driving, it may not be visible to you (because you're not at the front of the queue) or memorable (because it doesn't cause you to change your route).
I see people do crazy things all the time just out of impatience. People even fully enter the intersection sometimes (when they're going straight and have a red, and people turning currently have a green arrow), it's nuts. And then people will pull up behind them, locking them in. So if someone ran a light, there would be no way to avoid a collision. (Obviously you shouldn't run lights either, but people do.)
My philosophy is that any complex system can suffer at most 2 faults without a failure (as a rule of thumb). So when people push the boundaries like this, they're expending the buffer we need to avoid collisions caused by honest mistakes. If someone pulls into the intersection, someone pulls behind them, and virtually anything else goes wrong, there will be a collision.