I agree with the be careful what you wish for points.
Having our house renovated at the moment, and tradespeople just being able to park is a Godsend.
We don't have a car, we use the Zipcar. There is no issue with parking on our street.
But we are below the rat run prevention barriers (in our case south of Honor Oak P station). When you're on the station side of those, it's a different issue - and there is commuter parking. Albeit not in huge numbers.
So if there is ever to be CPZ etc., I think it should be over only the relatively small areas it's needed, and for deterrent hours only rather than 24/7. CPZ charges no doubt only go one way - up! - and obviously create potential for revenue for the local authority with zealous/over-zealous enforcement too.