This doesn't work by the way, but they really did try it.

Inevitably something goes wrong, delaying a train, and then it's dangerous because the timetable says it's clear ahead of you but it isn't.

Eventually the absolute block system was invented. You track where a train actually is, and don't allow more than one train to be in a "block" of track. But that took a whole bunch more technology and a whole lot more deaths to invent.