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> In rail, everything happening within visual range is basically too late to even bother

Not really. EMU passenger trains, such as subway trains, do have good acceleration times--good enough that it's limited by passenger comfort, not by physical hardware. This limit is about 1 m/s², with emergency brake conditions reaching 3 m/s² (note that the latter does imply several passengers are going to be nursing injuries--there's no seat belts after all). That's roughly comparable to typical passenger vehicles.

Freight trains have much longer braking distances, but that's a factor of 10,000 tons moving at 50mph has an insane momentum combined with relatively few axles being able to contribute to stopping force.

The main reason you need large distances between trains: switches. To control where a train goes requires moving a physical piece of infrastructure at the switch. You can't move the switch until the previous train clears it, and you don't want to let the subsequent train reserve a path over it until it switches into a new position--if the switch gets stuck in the middle, the train derails instead (or worse). The "brick-wall" principal follows from this situation.



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