Whether the chargers are public or private there will still need to be more of them than there are presently gas pumps and there will need to be an increased energy supply and transmission capacity. That is a decades to century long infrastructure project, and there is no way the US will go electric 5 to 10 years after Europe. I don't think it will ever go to electric dominance, that just isn't going to happen in the US as a whole.But my prediction is that per driver, fewer public charging stations will be required than gas pumps today - even if charging away from home takes triple the amount of time than filling with gas. I believe the number of charges at public stations will be far fewer than the number of fill-ups at gas pumps.
There is no need for assigned parking. Technology will take care of that - the charger will communicate with the vehicle for billing purposes.