I usually ride my bicycle to the train station for uni and then get a lift home in the car from the train.
Also you may want to recognise that electric cars aren't overly expensive at the moment, they just don't have the same mileage (which is slowly changing with new batteries and advances in the capture of solar power). Also the methods of producing electricity can be extremely clean and in some cases actually benefit the environment by doing it (using methane or other natural gases for instance).
If the government were to invest so much into public transport to make it that accessible then where are they getting so much money from? As you stated electricity is apparently expensive so they would have to have extremely high prices to compensate or to use gasoline which would go against the reasoning of taking public transport instead. I guess natural gas would be an option, but why wouldn't we just use that in our cars instead if it is so cheap?
I do realise this is hypothetical but it seems too far fetched if you use a little bit of logic about it.