I think the typical fear actually goes the other way -- that infrastructure won't be able to handle increased peak demand, leading to a lot more gridlock/pollution, longer commute times, etc. when more people are driving.
Reducing the need for parking in city's should have a massive net positive impact. In time we should see self driving electric cars on electric highways which can mean unlimited range and vastly reduced pollution. Even if all you do is drive one person to and from public transit that lets a wide swath of family's go one car without public parking fees.