I don't know how much that will matter in the states, but when we tried it in Denmark (in some towns), it meant people took the bus more - but it was those who would otherwise take their bike or walk, not people who would otherwise use their car.

It makes sense too. I can get a 30 day pass to drive with public transportation as much as I want, but it is so much faster to take my car that I essentially only take it (prepandemic).