Edit: If every country on Earth had India's emissions per capita, we would be cutting global emissions to
less than 25% of what they are today.
Emissions per capita are relevant if you want to discuss a realistic expectation of how low a country's emissions can go. They are also directly relevant: every citizen of a country must be fed, must be given electricity, must use transportation, and must consume goods - each of these cost CO2 in quite direct proportion to the number of citizens.
For example, China has a lot of room for improvement, but India does not, as it's already at lower emissions per capita than half the world (much lower than any EU country, for example).
Global warming is not exclusively the problem of the global south. Poor people in China or India have the same rights to affordable electricity as people in Norway or Germany, which have higher emissions than China per person, despite the fact that they have outsourced plenty of emissions to China.
Overall, if say we needed to reduce emissions by 50%, countries with higher emissions per capita will likely have to reduce MORE than that, as China and particularly India would incur much more harm to their hundreds of millions of citizens than Germany or the USA if they were to significantly reduce emissions.