re: Yellow lights need to last longer on 55 mph roads.

Almost all clearance intervals are developed based upon approach speed and the distance required to clear the intersection. The equations are followed very closely as miscalcs are the single quickest way to get people killed/injured involving at-grade intersections.....and plaintiffs attorneys hit that first.

On the slamming brakes, the issue is called the Dilemma Zone. It is an area where the yellow indication in shown and a car is at a point where it cannot stop within the time/space allocated. Engineering has come a long way to correct this and the advanced detection methods have helped tremendously. Still, DZs exist.

ETA: the clearance interval is not only yellow but All-Red indications. So, while you enter an intersection as it transitions to red, it will likely remain for 1-2 seconds on all approaches seeing a red ball.