Just a couple of observations.
1. Bike paths primarily see recrational activity.
2. Bike commuters almost universally started out as recrational cyclists.
3. More bike paths mean more recreational cyclists.
4. More rec cyclists provide a larger pool to possibly have more commuters and others that use bikes for transportation.
5. More commuters and such the more bike friendly infrastructure will be needed and hopefully funded for them.
6. More people on bikes is less people on cars.

If all this money does is provide facilities to introduce people to cycling is a safe not threating environment, then it's money well spent. Just my opinion.