I prefer to see it as regular signals designate the next segment as a segment where trains are allowed to wait. If you don't want trains to stop in that segment, don't put a regular signal in front of it.
And of course you don't want trains stopping on intersections, because they'll block everybody, so you always put chain signals in front of intersections.
The train needs to reserve the whole next contiguous sequence of chain signals to be able to go, so the foolproof method makes it sound like each train reserves the whole path from one station to another. It makes sense, but I like to do the optimizations, then, and allowing trains to stop in longer stretches where they can.
Chain both in and out is supposedly the foolproof method, and apart from stations, rail signals are just an optimization.
Though I've played a lot of Factorio, I've never really felt the need to dive deeply in to signals, and I'm happy to just use the foolproof method and leave more optimized solutions for those who need them.