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.
