Nice. You take a statistic which can be compared between all countries and change it so that it can't.
Per capita shows how much, on average, each person uses. All countries can be compared against each other.
Per km2 cannot be compared between countries as is dependant on population density. To compare all countries, you need to divide that number by the population density, which would actually give the emissions per capita. You can't compare statistics that can't be compared.
I could post up examples of total CO2 emissions. However, they cannot be compared. The USA would have a very large value because it's a large country. The UK would have a much lower value because it's a much smaller country. The total CO2 emissions is dependant on the total population of the country.
You can only compare the per capita data with each other or you take into account other factors like total population or population density.