Maybe they drive a more efficient car, but they own much larger houses which are heated or cooled consistently, they travel a lot more, and they buy things with embodied carbon emissions.
That's close to impossible to implement. You'd need to track production and usage of everything in an extreme detail. Plus tracking all purchases (items + services) to a given person. So complete state surveillance of citizens. Globally.
You don't need state surveillance or tracking purchases. You just need to get to the source of the problem. Hydrocarbons leaving the ground.
At the hydrocarbon level, it's much easier to track. Oil and gas is mostly extracted by very large corporations and transported by large infrastructure. You don't care what happens to it once you've produced it - but you do need to put a levy on the hydrocarbons before they're sold on. The people who use those hydrocarbons all have higher costs which pass on to customers.
The biggest problem is international borders. If another country isn't applying carbon tax, then you need to make an estimate of the embodied energy of a product at the point of import. Or encourage them to tax carbon. But neither of those require surveillance. Once the product has been imported, you don't care who buys or sells it because the tax is already paid.
For a carbon tax, I think you only need to track imports, and domestic extraction of coal, petroleum, and natural gas.
What problem was solved here? None.
Finally a good use for tariffs!
Increasing the tax on aviation fuel to $2/gallon wouldn't produce massive shifts in the next several elections, therefore it's easier to implement.