Well, "poorer" people is another social problem when there are rich, but not fit for leaders, decision makers. E.g., if the carbon tax was used to insulate homes, fit heat pumps, provide adequate EV public transport, then a tax on fuels would benefit those on low incomes. Obviously, there are policies that can be developed to make the rich pay for the costs of phasing out fossil fuels & biofuels.
Trading schemes are generally promoted by polluting companies as a 'smoke screen'.