I think a more useful metric is per unit of GDP. ...because then it becomes an efficiency metric. "How much wealth can we create with X amount of CO2".
First of all it suggests that wealth is the be-all and end-all of human progress. It also implies that wealth creation is equivalent wherever it happens - that somehow if a place is more efficient at creating wealth than it should be privileged.
Finally, of course, this means that poorer countries that produce less wealth will almost certainly be less efficient by this metric, and hence should be penalized (of course, we shouldn't mention that a lot of their production actually ends up being consumed by the rich-world which can this way claim to be highly CO2 efficient).
but then very poor countries will never be able to get to the development level of the rich countries because they’ll be energy limited. Buying a car (even if electric) could push them over the quota. Where as folks in the west can continue driving their giant SUVs.