You are 100% correct, this is known as the carbon-fee-and-dividend[1] scheme, and it has a number of advantages for all sides:

* It does not further harm poor people - as everyone receives an equal dividend, it makes a bigger impact the less you have. * It provides a long-term, predictable carbon cost. Business can plan many years in advance and not be caught by surprise. * It's effective at reducing emissions (not the exact scheme, but see Australia under the most recent Labor government, before the repeal of a carbon price).

I'd encourage everyone interested to get in touch with the Citizens' Climate Lobby and pitch in.

[1] https://citizensclimatelobby.org/basics-carbon-fee-dividend/