This idea seems to incur very high bureaucracy costs. What are CO2 producing activies? How much are each of them taxed? Who measures the tax and is responsible paying for it? Etc.
One selling point of basic income is that there's no loopholes and there's very little bureaucracy costs, therefore a larger portion of the money is actually used for consumption instead of doing unnecessary (for society) work.
Of course there are details to work out but it is fundamentally a solvable problem. A tax on any coal natural gas or oil should cover most of the bases (per ton of carbon contained). If it is being purchased for a use that won't end up in the atmosphere (IE carbon capture and storage), the burden is on the purchaser to prove the case for a tax write-off.
I don't think there's a reason to couple a CO2 tax to basic income. You can create a CO2 tax separately from basic income, as it has enough opponents as it is.
I suggested coupling them because I was looking for something that fits, "Solve as many problems with one go as possible, getting rid of as much legislation as possible."
If you create a significant CO2 tax separately from some specific program, like basic income, the fear is that it will be (and will seen to be) just a general supplement on government spending. Which has a tendency to grow until it cannot, so you're just putting off an inevitable crunch that we're already bumping up against.
But if you tie them together, the pain of the tax is balanced by the pleasure of the income. And people have been shown to enjoy that sort of thing. Witness the popularity of tax refunds, even though getting one is strictly worse for you than not getting one.
You don't need to tax actual CO2-producing activities. You just tax the production of CO2-containing fuels. The price is passed on to the buyer who produces CO2 with them.
You can then offer tax credits for CO2 capturing (with the burden of proof on the claimant).
One selling point of basic income is that there's no loopholes and there's very little bureaucracy costs, therefore a larger portion of the money is actually used for consumption instead of doing unnecessary (for society) work.