Moreover, it ignores that most reductions are taking place in countries with the highest per capita carbon emissions
Yes but those are also the countries with stagnating or decreasing emissions per capita, while the ones with rising emissions are also increasing in population. These compounding factors can cancel each other out when looking at net emissions.
Let's say right now we have 10 people from the u.s. emitting 10 tonnes of co2 and 10 people from the developing work emitting 1 tonne of co2, for a total of 110 tonnes of co2.
Now let's say in 50 years we now have 8 people in the u.s. emitting 8 tonnes of co2 and 12 people in the developing world emitting 5 tonnes of co2 for a total of 124 tonnes of co2.
This isn't to let western countries and their lifestyles off the hook, or that developing countries don't have a right to increase their standard of living like the west did, just saying populations stagnating or decreasing won't necessarily help climate change.