People forget that transportation has an amplification affect across your entire economy. It takes all of the friction caused by traffic and removes a percentage of that. Helping not any one individual but everyone. It's understandable that it's harder to wrap our heads around something that isn't directly profitable when we're raised that way... but all the evidence and research is clear. Public Infastructure not only is the right way to help people, but is the best long term economic solution to transportation.
Further, who do you think pays for roads? Or their repair? Road infastructure is heavily subsidized and far more expensive than any public transportation project. The big difference? You won't hear politicians making a stink about it