This isn't a binary. We need both robust public transportation and electric cars (with an electric grid supplied by renewable energy). Public transportation can't take you anywhere at anytime -- it's all a game of statistics and demand. If 12000 people want to go downtown at 7 pm, and 3 people want to go the opposite direction to get to work to start their night shift, you're going to see buses and trains headed downtown but not the opposite side of town.
Public transportation is best served for commutes and travelling to popular areas, and that's where the majority of emissions are coming from. Cars can supplement with everything else
They are, but only in specified routes. The issue is the areas they don't hit because there isn't a ton of demand. That said, someone else mentioned a taxi type public transit service, and that would solve this perfectly.