Regardless, transit should pay for itself in the same proportion that roads pay for themselves. Transit has per-use or per-distance fees around using it, but are also subsidized by the government. Road travel has per-use or per-distance fees (tolls, gasoline taxes), and are also subsidized by the government. I'm sure we can continue to find a balance for all of those numbers so no one is disproportionately burdened to support their needed mode of transportation.
Public transportation is used by people from all walks of life. Not just office workers - cooks, nurses, artists, school teachers, police officers, even employees of trade companies... and every citizen benefits from reduced traffic, lower infrastructure costs, and better health.
Using car taxes to fund public transportation would not materially impact the carpenter. They'd just charge a little more. An absurdly high $1000/year tax spread across 50 clients is merely $20 per job - a more realistic $200/y tax would add $4 per job. Considering that public transportation increase average disposable income, the market can easily absorb that cost.
And so too can the office workers. To charge one group for the benefit of another, based solely on the manner of their employ, is the definition of unfair. This is what progressive taxation is for, not use taxes.
For businesses that require car usage, the tax is merely an operating cost. There is no impact on profit as operating costs are passed on to the consumer.
Of course, allocating that revenue is still subject to local voters' wishes.