It also dodges the real issue in the bay area, which is housing. Commutes are long because most people can't afford to live next to their jobs. If we stopped restricting new housing and taller building, then the number of cars on the road would decrease.
Furthermore, there are innovations coming that might shorten commuting (e.g. things like Hyperloop, although I have no idea if that's viable) and self-driving cars (which let you read/work/etc while commuting). The government is not going to be able to deploy $100b better over the next few decades than the private market.
Finally, the rise of remote work might mean a lot of professions commute less in the future. My prediction is this just going to be an exercise in setting $100b on fire.