You're also indirectly taking money from big corporations and putting it into the pockets of citizens, which has been proven to be one of the most effective methods of stimulating the economy.

It doesn't matter. Pay debt. Dig holes. Build bridges. Just rebate it to whoever on a per-capita or per-tax-paid basis. Literally do anything with it.

The point is to incentivize conservation, not to raise revenue. You could get the same thing with a regulatory carbon penalty too, but it's simplest to administer as a tax.