You'd have a hard time getting a CO2 tax passed because it would just end up going into the general fund and get spent on pet projects, not on anything that really addressed CO2 emissions, or helped with the cost of alternative fuels or vehicles.
A carbon tax would work if you burned the money. Bonus points if you captured the CO2 from the fire :)
A carbon tax serves to connect our intuition to our logic. We logically know that, somehow, the sum of all our disparate little actions is responsible for global warming. But the feedback loop is notoriously long, and complex. And humans are no-to-ri-ous-ly bad at properly valuing that. We couldn't do it to save our lives, or that of our species.
Furthermore, it helps break free from the tragedy of the commons, where every independent agent makes a game theoretically optimal move, to the detriment of the global system. No amount of proselytising or appealing to humane sensibilities, no amount of ecological lucidity or sudden flashes of intuitive insight into that awful feedback loop, would ever solve that problem.
No weapon works better against overfishing than quotas. Not necessarily a tax, but leveraging the market similarly.
No weapon works better against carbon emissions than a carbon tax.
Pigovian taxes are powerful weapons in a market oriented society. Very, very powerful. This is why vested interests will do absolutely anything to prevent them.
Doing something useful with the money is just a tiny cherry on top of large cake of success.
This is very under appreciated. A lot of potential taxes aren't actually collected because people alter behavior to avoid them. For a carbon tax that's the point.
I'll also say the behavior you want to alter is not 'buying carbon based fuels'. The behavior you want to stop is people buying gasoline powered cars and natural gas fired furnaces. Which means what you want is a excise tax on those things not the fuel itself. Because when someone buys a gas powered car they commit then and there to emit 100 tons of CO2. So make the pain point then and there, not in the nebulous future.