There is absolutely no "shortcut" for cities to skimp on having sufficient transit infrastructure to get people where they need to go. If you underbuild, people drive cars. If you overcharge, people drive cars. If you restrict car traffic, people simply don't move or work in your city and your economy dies.

One way to balance between free ride abuse and people not using the trains because they have a car is to give residents the "average" number of rides a commuter would use in a week to them every week for free. Maybe even give people who don't own motor vehicles more free rides as a "thank you" from the city for not making them maintain the road and parking infrastructure for you.

But any city that is not expanding its transit to meet demand is crippling its own economic potential. Its a shame that pretty much every US city is guilty of this but most of the US government is designed to self-sabotage things like publicly run transit anyway.