Rewards for Those Without Cars

The petition is entitled reward people who don't have a car and the explanatory notes say

"Why not reward people who don't have a car (through poverty or through choice) with an annual benefit that would make using public transport more affordable? Paying people £500 or £1,000 a year for not having a car may make it easier for people to give up their vehicle if they don't use it much and reduce the temptation to travel short distances."

There's a lot to be said for a carrot-rather-than-stick culture. The only thing is - this is only going to be an encouragement to people who really can practically get rid of their cars. Most people really, really feel they can't. So while this would be a nice inducement to people like me (who already don't have cars!) it's not going to do a thing to encourage people like my mother (who needs her car to work) to use public transport more often.

Surely a better use of the money would be to make public transport cheaper for everybody, to encourage people who need cars some of the time to minimise their use?