There wouldn't have been any improvement for the poorer paid under TIF, all we were promised is what we now have, more bus lanes and 100 yellow buses spread between hundreds of schools, the TIF bid was a con as the majority of the public in Manchester realised which is why it was thrown out with a vast majority.
Bus fares would not have reduced, there would still be no way of getting to Trafford park without a car, you would still have to pay an extortionate amount to take your children on a bus.
So all of the above means yes the poor paid have to run a car and car share as public transport is just to expensive.