The "failed" part of the experiment is that far fewer people ride bicycles in Australia today than did before helmet laws (edit, incorrect, it's per capita reduction, not absolute) in absolute numbers, not even per capita, adjusted for population growth.
The laws are successful in that they get people to wear helmets, but they are an abject failure in terms of participation in cycling.
Gonna need some evidence for that causal link you're suggesting here. Counterpoint: Plenty of bike paths get plenty of use. We didn't even have these bike paths when the helmet laws came in.
I misread the thing I was looking at, it is per-capita, not absolute. Here is a graph of the number of people cycling to work, the peak is the late 80s/early 90s before the helmet laws:
The laws are successful in that they get people to wear helmets, but they are an abject failure in terms of participation in cycling.