If the intention is to implement a carbon tax, I see no way of doing so without some relatively accurate measure of carbon output. Without that you are taxing not carbon but instead something else.

Sensible carbon tax proposals are generally based on extraction, not consumption. There are only a limited number of companies mining coal and drilling oil. Those can be measured fairly easily.

The simplifies the problem technically and complicates it politically, at least in the US. Those hardest hit by a tax implemented that way are friendly with the elite of the US, so much so we have been at war with their enemies for decades.