you forgot (3) an efficiency gap. No government or quasi-governmental organization can deliver this program without massive leakage. Look at Canada: carbon taxes go into general revenues, and some portion of it gets paid out of general revenues. It also doesn't matter if the payment is a redistribution or an ad buy for a terrible commercial on the CBC - it's all fighting climate change!
You'd wish instead of "seeing like a state" organizations would learn to "see like a consumer" and be able to recognize that a terrible commercial is a terrible commercial!
I think the efficiency gap is less than with other approaches. Rather than privileging electric cars we should reward people the same if they save carbon by buying an electric car or riding a bike or if an industrial process is replaced by one that is naturally carbon free or if you take the carbon out of the stack or if you take it out of the atmosphere. The market should decide what is the most efficient.
(Note another 'efficiency' concern people have is that you don't want to pay people $400/ton to store carbon from fermentation at an ethanol plant that is unusually cheap at $40/ton because you get nitrogen-free CO2. People seem to have a moral problem with that, first fundamentally, second because the ethanol plant is problematic in other ways)
It's better if the tax revenue goes back into fighting climate change but the point of a carbon tax is to punish bad behavior. Just by implementing the tax you're fighting the problem (in a small way).