Absolute numbers matter when considering the total CO2 budget for the Earth.

When considering how to divide that budget among the people of Earth absolute numbers for countries do not matter, because the atmosphere does not care about arbitrary lines humans draw on maps.

One easy way to see that per capita is the correct way to allocate the budget rather than per country is to consider what happens if countries split. Suppose we agree on a worldwide budget of 4 x 10^10 tons of CO2/year.

If we go by country each country's share is 2 x 10^8 tons/year. That would mean in a small country like Liechtenstein they could live a lifestyle that required 5000 tons/year/person.

Meanwhile, in the US we could only live a 0.6 ton/year/person lifestyle--about what Zimbabwe uses today. That's about 1/25th of the current US lifestyle.

That is not going to work. The US could hold a constitutional convention and dissolve with each of the current 50 states becoming an independent country, and at the same time make strong free trade and mutual defense treaties. They can call this the "American Union".

That raises the number of countries in the world, so each country now gets a smaller slice of that 4 x 10^10 tons/year global emission budget. Collectively the total emissions budget of the combined states in the American Union is around 8 x 10^10 tons/year. That allows the American Union to live a 24 ton/year/person lifestyle as a whole (which is 60% more than the current US lifestyle).

Of course China, which only gets a 0.16 ton/year/person lifestyle under the original country allocations could do the same thing. If they did the Chinese Union with the individual countries being what are now prefectures, that Chinese Union could have a 15 ton/year/person lifestyle (about the same as the current US CO2 emissions.

Each time a large country does this "split into a strong union of separate countries" thing the boost in how carbon intensive a lifestyle that union's residents can lives comes at the expense of a drop in what the rest of the world can have.

The limit of this is a world of thousands, or even millions, of micro-countries, each with about the same per capita CO2 allowance.