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:
https://www.researchgate.net/figure/Percent-cycling-to-work-...