Also, it might have been more challenging to schedule the trains and keep them from smashing into one another without some kind of a common timetable.
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.
"In the UK, the Regulation of Railways Act 1889 introduced a series of requirements on matters such as the implementation of interlocked block signalling and other safety measures as a direct result of the Armagh rail disaster in that year."