This is a good idea in theory, but there just isn't enough parking for all the cars on the road now.  You can't ban them without giving them somewhere else to go.

A lot of our housing, particularly in towns, were built way before people had cars, the roads are too tight to park on the roadside so they are forced to put two wheels on the pavement to allow the safe passage of emergency services and bin lorries.  Even with more modern housing estates, there isn't enough parking provided.  I find weekends particularly bad when most people are home that would otherwise be parked at work.  

The real answer to this is reducing the amount of private vehicles on the road - and I say that as a car guy & someone who is unable to use public transport!