The car in front needs to react earlier. He/she should have seen it early enough to make it safe, no?
Why is it unrealistic, besides the fact that you're following too close behind? If your line-of-sight is shorter than your braking distance, you are driving wrong.
Google shows two-second rule when looking for "safe following distance" - I was taught 3 seconds and it seems more reasonable assuming slightly over a second reaction time.