They should be looking at the signal that consists of a red lamp above a yellow lamp above a green lamp. While the green lamp is lit, they should keep driving and not slam on the brakes just because the little man in the crosswalk started blinking.

Yes I know that rear-enders are at fault even when the rear-ended did something stupid. In fact many driving accidents can be attributed to the stupidity of multiple parties, and the accidents described above can also be so attributed.

The driver behind them should be watching the car in front of them and be following at a safe distance. I don't see why you should run into the back of someone if they slow down for an intersection with 1-2 seconds left on the timer and they're at a questionable distance about whether they'll make the light.

It's as if you didn't even read the second paragraph, in which I also blamed rear-enders for rear-ending!

If the light is green, there's nothing "questionable". Either one will make the light, or one will have time to slow once it actually turns yellow. If, instead, one does something surprising and irrational, misfortune may result. In this scenario, as in many accident scenarios, both parties have driven poorly.