Scenario 1: You’re assuming that everyone is observing adequate stopping distance, has working brakes, and is adequately paying attention to slow down.
Scenario 2: You’re assuming that green means it’s safe to go and that the cross traffic light turns green simultaneously with a given light going red.
Let’s address the easy stuff first.
In scenario 2, if my light just turned red that means the opposite light just turned green. This isn’t how stop lights work in practice. Usually, both sides of traffic are stopped momentarily before a light turns green such that traffic in the intersection can clear. Also, if you see a stop light that’s red you are usually slowing down. In other words, right before cross traffic gets a green light they are either stopped or slowing down, assuming they can adequately pay attention.
Cars have mass. You don’t instantaneously go from 0 speed to speed limit. It takes a ramp up time. It is generally low risk to run a stop light immediately following a light change.
Now to address both scenarios, we have to talk about defensive driving.
Never assume someone is doing the right thing. If your light turns green, make sure cross traffic is slowing down before you proceed. Be ready to slam on your brakes if someone is going to blow through a red light late and at speed
You can’t break physics. If the person behind you is not able to stop and you can safely make it through the intersection, do so. Otherwise, pick the safer of two accidents and learn from your mistakes.