Europe also had a big military imperative to build railways pre-WW1: Trains let you move your forces faster, so you can build up a concentration of forces in one location to attack or reinforce a defensive line.
So no state in continental Europe wanted to be on the losing side of a railway gap.
This is probably a much bigger factor than usually thought. Military necessity will trump budget constrictions and property rights. Railways pre WW1, roads during and after WW2 and in preparation for the Cold War.
So no state in continental Europe wanted to be on the losing side of a railway gap.