Who gets to decide what the carbon footprint of every activity is? How is the surveillance of every activity performed? What is the performance metric to evaluate the success or failure of the system?
Corporations buy carbon, to a good first approximation, as coal, gas, or crude.
That's what you tax. Plus a tarrif on countries which don't do likewise.
Recognize that all your questions could have been asked about, say, sulphate emission regulation in the 1970's. (Or CFC's in the 90's). And that worked out OK.