But obviously the earth is comprised of sovereign states, and in order to collaborate you often need to convince those sovereign states that treatment is fair. Given that, if you want to adjust emissions by some divisor, I'd adjust it by land area. Land area is finite on earth. That means that there is some value of CO2 output / m^2 that is sustainable for the planet. That number is consistent. That number applies globally. That number can be a target for everyone. It also can't be faked – some "unreliable" country can't say "hey, global body, you think our population is 1B but it's actually 1.2B, so we get to pollute more". You can't fudge land area like that (there might be some marginal ability to do so, but obviously it is less feasible than with per capita numbers). This has the additional benefit of aligning priorities against worsening conditions in order to incentivize action now. Global warming is causing rising sea levels, which in turn means that countries are losing land area. That means that every year that global warming worsens, your quota will actually decrease.
Meanwhile, population is not finite. If you say to a country as part of an agreement to "get your CO2 output down to this level per capita", then it is a very real possibility that this country's population grows to an extent where that number you used last year is no longer small enough to stave off serious global warming. And that is the purpose of all this, no?
Obviously carrots and sticks will be necessary for any agreement to be effective (until it gets really bad), but either way I think emissions/unit land area as the line in the sand makes more sense than emissions/per capita.
An even better metric would probably be "emissions/unit arable farmland", as it gives weight to both land area and population, but obviously that is much more difficult to establish / less likely to stay static.