Strongly disagree. There are too many perverse incentives that work against transit. If there are a lot of car commuters (which there will be - plumbers taking their tools to the job for example) they have inventive to pressure politicians to reduce that tax - any voting block will always be more powerful than the distributed masses. Your transit operators need to ensure transit doesn't become too popular: the more people taking transit the less cars there are paying that tax.
Besides almost no transit rider is worried about costs. They are all interested instead in better service, so use all the money you can get - including fares - to build better service. This is long term what everyone needs.
Yes you do need a program for the poor. However the majority of your people shouldn't be in that program.