The idea is GDP is a measure of activity. So using per GDP allows you to see the efficiency which you are producing "value". That's not a terrible idea in general but it accepts a very narrow definition of value.
GDP is a really flawed measure of how well a society is performing. I wonder what it would look like if we used Gross National Happiness or Total Quality Life Years. Could also think about ecosystem health or biodiversity as a valuable output of a country but that's highly linked to CO2 emissions so wouldnt be meaningful.
Also worth saying whilst per capita is absolutely important as a measure for us to understand the performance of human economic systems the earth systems only respond to gross total emissions.