A respark zone would only push the problem elsewhere, then another set of residents would find they had nowhere to park, so they would also demand a respark zone, and so on. Ok, so there's loads of empty spaces outside your house, so you're all right Jack!
But the driving commuters don't all suddenly get on their bicycles and pedal to work. It just keeps driving the problems onto someone else's doorstep.
Some people do rely very much on being able to drive and park near their work / transport connection to work e.g working parents - there just simply isn't time between dropping off children to do the necessary bus catching, walking or whatever. And then there's picking up, when you're train is delayed or whatever - after school care do get very stroppy if you are late!
When I'm on school run duty, half and hour's walk is the nearest I can park to my work in Brixton because of all the parking restrictions. I have to leave work no later than 4:15 to collect my children by 5:30. Thank goodness for flexitime and a self-employed partner! However, some people might be forced to cut their working hours, go part time or whatever, so reducing household income - most unwelcome in the current economic climate.