Earlier quoted context omitted.
Not necessarily. Tax carbon heavily and then redistribute the tax equally among all citizens. Anyone using above average carbon net pays into the system, anyone using below average gets a net payout. Then markets, our most advanced coordination/optimization method can be utilized to figure out how to reduce our carbon emissions.
The goal is to reduce total use of carbon based fuel sources, not just redistribute wealth. While I agree that redistributing wealth should also be a goal, any solution that doesn’t lower total consumption is useless, so the pain of less consumption would be felt by anyone consumer more than average (which is probably everyone in the developed world).
We want the tax rate to be high enough to disincentivize carbon-emitting actions relative to carbon-neutral (or carbon-capturing) actions. But if government's ability to finance public operations is also affected, then we have a problem. The revenue-maximum tax rate is based on a completely different optimization problem than the carbon-minimum tax rate.
Making carbon taxes revenue-neutral decouples the two policy objectives.