Raising the price of gas negatively affects the working poor more than helps the environment. That subset of society may not live in an area accessible by transit, or their employment requires them to be in a different location than is feasible to travel to by transit.
In the short run. In the long run, the proceeds could be used to encourage the working poor to move to cities where they don't need a car. Given how financially terrible car ownership is for America's poor--between traffic tickets, civil forfeiture, police violence, predatory lending and collection practices, insurance practices, et cetera--I think it would be a net boon.
If we funneled as much money to mass transit as we do to vehicle infrastructure, there'd be no competition.
This is about deciding which kind of city you want and building the transportation options that fit that environment. Cities built for cars are very different from cities built for density and walkability. You can’t compare the two modes devoid of that context.