If people stop harder, they're more likely to get in an accident doing so. If you don't have ABS, stopping harder increases the odds that you'll skid. Also you're more likely to get rear ended if the person behind you isn't paying attention.
If you do that, you'll still cause more people to slam on their brakes to avoid running the red. Slamming on the brakes increases the risk of losing control of the vehicle, and of being rear-ended.
> It won't necessarily endanger the public if they add more delay between one light turning red and the other turning green.
This is usually referred to as a delayed green light. They are absolutely terrible for public safety.
There are drivers who look at the opposite light to get a cue as to when they should go.
It also pisses regular drivers off, because it looks like absolutely nothing is happening for everyone and they have to sit there and wait for no good reason. A yellow light, even a long one, at least shows some sort of activity and progress.