In terms of cost, public transportation is not that cheap, speaking in terms of $$. I pay more than $10 per day to ride the Metro in DC each day, and people who ride the VRE trains pay even more (closer to $15 per day). Those costs are subsidized somewhat by taxpayers too.

Other disadvantages: trains only go certain places and at certain times, so they are very inflexible. If my wife were expecting a baby and we needed to get to the hospital, I can't summon a train to our house but I could call a self driving Uber car at any moment. I live 15 miles from the nearest Metro train, so I have to drive my car for 30 minutes just to get to public transportation.

In terms of traffic lights, congestion, etc. caused by cars, I recommend that you read some of the research on self driving cars. They claim that traffic lights and congestion can be eliminated by self driving cars because the cars would have sensors that would allow them to coordinate their movement through four way intersections, so no need for traffic lights. Congestion on freeways is caused by rubbernecking, accidents, and the human need to have a certain safe distance between cars, another issue that would be eliminated by self driving cars.