This is simply turning on its head what is already happening, in order to make it more effective. The policy can have a degree of flexibility built in to it - for example, second cars for demonstrable long distance driving needs can be plug-in hybrids or range extended cars, otherwise they should be pure electric.
Here in the UK, as a third of households have two or more cars, this would go a long way to addressing pollution, climate change and energy security. As second cars are used almost exclusively for local driving (the most polluting and inefficient kind), this would be particularly effective.
As well as directing consumer purchase behaviour, such a move would also send a strong signal to auto manufacturers and investors. I know that we shy away from such directives, but this makes sense.
It is a policy that can be managed centrally, through government vehicle registration, and locally, through council street parking permits. Too big brother? Or too good to ignore? What's not to like?