> Theoretically, most countries emissions could go to zero with nuclear, wind, solar, hydro, and/or geothermal.
I think this is the bad assumption that is causing you to think emissions per capita are not important. Power generation is only a fraction of the problem. Most clearly, GHG emissions from cows and pigs will not go down even if all electricity energy is produced with 0 emissions. Incidentally, India's widespread vegetarianism may be a big component of how its emissions are so low.
Then, transportation will not magically become electric even if the whole grid is green. Perhaps cars are a solved problem, but electric trucks, electric air planes, and electric cargo boats are definitely not solved problem, not for anywhere near today's costs.
There are of course numerous other industrial processes which emit massive amounts of CO2 that can't be electrified at all - cement production, smelting, plastic recycling, many chemical processes etc.
Also, new nuclear, hydro, solar, and wind are not competitive with already built coal or natural gas power plants - so moving to a new entirely green grid would massively increase the costs of electricity, which in turn will increase the costs of basically all consumer goods.
And while many in the USA and Europe could afford to pay twice the price of electricity and all basic necessities (though nowhere close to all), few would in India or China.
Now, would it be important and good to pressure and fund China, US and India to replace what they can of their electrical grids with nuclear and other green energies? Absolutely! But it only addresses a small part of the problem, and does so at tremendous cost.
Edit: electricity generation accounts for ~50% of China's GHG emissions, ~35% of India's and ~25% of the US's. So even entirely greenifying their grids will not reduce world GHG emissions by anywhere near 50%.