Aren't braking distances so large because of the massive amounts of mass in motion? Inertia, etc. Even high certainty of track friction wouldn't change that.
Also, I don't think it's ever safe to be closer than braking distance because the bahavior of the train ahead is never guaranteed. There's always a chance somebody parks their car on a rail crossing or some other sudden stopping-event occurs.
No, they’re very long because steel wheel on steel rail has much much much lower coefficient of friction than rubber on asphalt. If they brakes any harder they wheels would just lock up and skid, both running the wheels AND taking longer to stop than a normal braking application.
Also, I don't think it's ever safe to be closer than braking distance because the bahavior of the train ahead is never guaranteed. There's always a chance somebody parks their car on a rail crossing or some other sudden stopping-event occurs.