Carbon tax is unusual in that it has a major benefit simply by suppressing consumption.
If an alien civilization invaded earth and imposed a carbon tax, and took all of the proceeds back to their own planet, then we would still be better off.
Governments don't have to profit from it. In fact to get the desired effect (less carbon) the tax should be revenue neutral. It should be used to fund UBI or give everyone a tax credit.
If an alien civilization invaded earth and imposed a carbon tax, and took all of the proceeds back to their own planet, then we would still be better off.