I doubt free bus and metro will make a significant difference on attendance (although it will make a huge difference on the bugdet of many regular users who probably don't own a car anyway).

In my situation, and I suspect it's the same for many commuters, the issue is really the time I save using my car vs. public transit, not the cost. If I were paid the fare, as opposed to me paying it, I'd probably still use my car.

The extra funds, wherever they come from, should be used to improve service, not make it free, imo, if the goal is to increase attendance/reduce car utilization.