> even in the worst case of a conductor missing a red light at full speed, the safety system has enough time to stop the train before it crashes into the train ahead

For legacy systems that's not generally true, especially outside of rapid transit applications. This is because most legacy train protection systems can only intervene (if at all – some systems like the British AWS only require the driver to acknowledge a warning and don't actually stop the train even if it passes a signal at danger) when the train actually passes the signal, and at that point it's already too late and a mainline train at full speed will still require several hundred metres or even up into the kilometre range to come to a stop.

Spacing signals that far apart is impractical (it's not just about the signal-to-signal spacing on the plain line, but also how close to a junction signals can be placed and things like that), so most mainline railways didn't bother and only provide a limited "overlap" that gives some margin for mis-judged braking and similar incidents, but doesn't cater for a full-speed signal overrun. (And some countries like e.g. the Netherlands don't really do overlaps at all.)

Reliably stopping trains within such a limited (not full braking distance) length overlap requires a train protection system which can react not just when the train actually passes the signal, but also if it approaches the signal too fast to stop in time, and only a limited number of legacy train protection systems possess that capability (and even then maybe only in a partial fashion).

Things are somewhat different on rapid transit-style railways, where lower speeds mean that a full-length overlap (to go hand-in-hand with a simple trainstop-style train protection system of the day) isn't quite as ridiculously long and more practical to implement, and the combination of frequent trains with high passenger loadings in constrained surrounding (and therefore bigger risks in the case of accidents) also provided a higher impetus for improved safety measures than on mainline railways even one hundred years ago.

> It has the obvious disadvantage that a lot of capacity is wasted by the requirement to have one entirely empty block between trains

Even with modern cab signalling trains are usually spaced apart based on absolute braking distance (i.e. even if the train ahead came to a sudden, instantaneous stop, the following train could still safely stop. Even if you wanted to be more adventurous and allow spacing based on relative braking distance, a set of points/turnout that requires changing between successive trains effectively acts as a stationary obstacle, effectively returning you back to absolute braking distance.) The capacity loss with conventional signalling happens because the actual spacing then needs to be quantised and rounded up based on the actual signal spacing.

> spaced at least a full brake distance from full speed apart.

Sub-braking distance block lengths aren't anything too unusual, though with conventional signalling there's usually a limit to how fine you can sub-divide your regular braking distance. With more modern systems on the other hand, simulating "moving" block by just providing a large number of very short fixed blocks has been done and is entirely practicable. The motivation for true moving block is hoping to save on the installation costs for axle counters and suchlike.