All you do is turn it into a flat check that everyone gets once a year. The rich would literally subsidize everyone else. Most people would make money from the tax.

Also, you add in a cap and trade market and eventually reduce the limit to zero. Credits can't be generated unless you literally bury non-volatile, non-decomposing carbon 500 meters or more under ground.

I mean, what is your goal?

If your goal is to stop climate change, you should tax carbon. Making it a progressive tax isn't totally unreasonable... but it seems like an unnecessary complexity, since you are essentially crossing a sales tax with a wealth tax - so everyone would need to say how much wealth they owned every time they bought anything in order to figure out how much they would be taxed. Especially since the tax should increase each year to make carbon more and more expensive. Also, most carbon tax proposals take the fee-and-dividend model: all carbon is taxed equivalently, and then all citizens recieve an equal dividend from the money collected. So basically, every time Elon flies his jet somewhere, you get a free burrito.

If your goal is to reduce wealth inequality/remove the power accumulation of billionaires from the world, then you should make some sort of wealth tax. And then once you took all Elon's money away, he wouldnt be able to fly his jet anyway.

I think these are both important problems. But that doesnt mean we need to solve them both at once, nor that they will both yield to the same solution.