The basic problem is that they had built a domesday machine in Europe, which was the mobilization schedule.

After the Franco Prussian war people realized that the next war would involve massive armies full of mobilized (conscripted) men and the country that could mobilize first would win. Countries spend decades planning for this by manufacturing enormous stockpiles of uniforms, giving their entire male population military training, etc.

But the mobilization schedule for even the fastest country was still measured in weeks, but this was a process where days count. Basically once the decision was made to mobilize millions of people across an entire modern society would leap into action transforming itself into a marshal society. Millions of people getting called up, trains full of equipment going everywhere.

Turning off a mobilization that was in progress was fairly difficult to conceive of, so once the decision was made the flywheel would take over, but decision to mobilize had to be made in a pressure cooker environment where hours mattered.

The death of the duke wasn't the "cause" of WWI it was the starting gun for a race where the horses were all waiting impatiently at the starting line.