Fees are an effective way to shape behavior. Charge for the things you want to discourage, don't charge for the things you want to encourage. Charging use based fares discourages people from using the transit.
Because transit and bicycles are the most cost effective and energy efficient ways to move people, those things should be paid for with fees on cars. Toll the roads, and charge congestion pricing. Then use that money to pay for the free to ride transit.
The neoliberal idea that things need to pay for themselves is a cancer. My state really takes the climate seriously, or so they claim. But they actively discourage drivers from reducing their carbon output by using transit, or driving a hybrid or EV, by charging extra for those things specifically.
Make the busses and trains free and the cars costly.