Free isn't free. If it costs more time and effort than the equivalent (because the equivalent is more reliable, gets you within a block of your destination, and runs 24 hours a day) then "free" public transportation is still more expensive than the equivalent. Even a poor person who can't really afford to own and operate a car (witness the predatory reposess-a-car loan scams) will drive a beater to commute because the alternative is losing their job because they aren't able to get to work consistently on time.
If on the other hand, public transit is reliable (trains every 5-7 minutes, so you don't have to arrive 10 minutes early to avoid missing a train and waiting another hour for one) and the alternatives have heavy costs (looking for parking downtown that doesn't cost $$$, and enduring traffic in/out of a venue) then public transit is a no-brainer. This unfortunately doesn't happen due to the chicken and egg dilemma of modern urban planning - mass transit is a money-loser until you hit a certain population density, but to achieve that level of population density, you already need to have mass transit (otherwise that level of density is unobtainable because you've locked it up in roads and parking lots in order to serve the levels of population density leading up to that point.)