Or, and this is a controversial view, maybe some homeless people could be helped through cheaper access to cars. As part of my job I have recently sat through many days of cases at a local courthouse. In our rural area, judges are loathed to revoke a driver's license because they know that doing so renders a person effectively unemployable locally. If someone doesn't have access to a car, and therefore cannot find work, perhaps there is a place for giving them better access to a car.
(Anyone saying that the answer is better public transport, that isn't an option here. Rural area. Most work is in farms/oil fields/military. 24/7 bus service over thousands of square miles just isn't ever going to happen. No car or no cellphone = No work.)