I can imagine a few ways it can go sideways:

1. People start making perfectly walkable or bikable trips by bus

2. People start making trips they didn't need to make at all

3. Public transit becomes dependent on public funding, which may fluctuate with economic downturns -- whereas a private company would be more free to compensate

As a practical example, Tallinn, Estonia introduced free public transit some years back. Oddly enough, it had almost no effect to car usage although public transit use increased.