A given person will not inevitably get back less than their tax burden, people on average will get back less, but I'm pretty sure the median person will get back more. People who eg. fly a lot will get back less, those who live relatively modest lives will get back a good bit more. The wealthy will disproportionately bear the brunt of a carbon tax, because they tend to live much more energy-intensive lives than the median person.
Emissions scales very sublinearly with wealth. Someone who is 1000x richer than average isn't going to live in 1000 houses, eat 1000x more beef, or drive 1000 cars simultaneously. This means that they're in a much better position to simply eat the cost of a carbon tax while the poor and middle class will actually have to make the sacrifices to reduce emissions. Even if they're technically be ahead monetarily, they'd feel worse off because they have to organize carpools, turn down the thermostat in the winter, etc.
It's true that someone rich won't be especially bothered by fee-and-dividend, even though they're paying out more than they're getting back. It won't be an effective tool for reducing the emissions of rich people.
It's also true that a person with lower-than-average emissions will pay out less than they get back. They'll have a strong incentive to reduce emissions, but even if they don't reduce emissions they'll be better off than before. These people will be the majority.
The people who might feel worse off are those who emit a bit more than average without being rich. They'll need to modify their behaviors if they want to come out ahead. Of course that's part of the whole point.
A lot of people might actually be ok with changing their behaviors, if they know everybody's doing it so it will actually make a difference. Right now we have this public goods situation where the outcome is going to be the same regardless of what you personally do. Dealing with public goods situations is the main reason for taxes in general; it's hard to fund roads with voluntary donations, so most people are ok with paying taxes for roads.
The other benefit of fee-and-dividend is that it makes low-carbon energy sources more competitive. It's not just about getting people to carpool or whatever, it's about getting fossil fuels off the grid and the roads, because they just can't compete.
Of course if that works, the end result might be higher prices that don't get reflected in the dividend. But we don't end up in a apocalyptic nightmare, so there's that.
Rich people easily produce 100 tons of CO2 emissions or more per person. If they eat the cost of a carbon tax with a carbon dividend that is effectively a donation to less wealthy people.
Wealthy people own businesses and those businesses have a strong incentive to reduce emissions, when they do, they end up reducing the tax burden on their consumers.
You’re not wrong about the sublinearity, though someone maintaining a $20M mansion on 20 acres is going to use many times the energy maintaining it, especially when you consider the materials used for maintenance.
The average person wouldn’t have to organize carpools, though it’d certainly be incentivized - at least at the beginning, I’m assuming most wouldn’t, so not doing that, you’d still be a net recipient of tax money. But part of the whole point is that we can’t continue living exactly the same way, if we don’t want to destroy ourselves, and especially our children.
