This is where you are probably wrong and which so often is used in the narrative of "things are getting better". You make an implicit assumption that this development will go on. It probably won't. The reason is climate change.
But as is the case with automation predictions and massive net job destruction, it hasn't happened yet. So it's possible we're wrong about such predictions. We've been wrong in the past about environmental doom and job loss.
Or maybe not this time, but we should keep that in mind and be a little bit skeptical about our current state of knowledge when predicting the future. It would be one thing if the trend was clearly toward things getting worse because of climate change. But it's not so far.
Someone tell Fiji, I'm sure they will be happy to hear that:
https://unfccc.int/news/how-fiji-is-impacted-by-climate-chan...
https://www.salon.com/2012/09/19/first_village_relocated_due...
Not all predictions are equal. We're a lot better at modelling things now than we ever have been in the past. That's not to say we're definitely right this time, but the probability that we actually are right is much higher than at any point in history.
Or not. After all populism and demagoguery is extremely powerful (see religions).
The reason isn't climate change.
The Central African Republic has just come out of a civil war. Of course things are going to improve rapidly, because that farmer that was in a refugee camp can now go home and grow enough to barely feed his family.
You can't extrapolate that out to the CAR overtaking first world countries in a generation simply because that farmer hasn't been educated to do the jobs that the economy would require, neither probably will his children.
That's before getting into things like infrastructure, rule of law, etc, etc, etc.
Edit: To clarify, I don't disagree that climate change will probably hurt the poorest countries disproportionately though.
economists think in curves - starting from a low base it's very easy to improve fast, but the rate of improvement drops off as it nears the global average.
ecologists think in straight lines - the rate of improvement is x/year, so in 50 years the improvement will be 50x and they'll be richer than Sweden, who are only improving at (x/10)/year.
The parents contention is that climate change will prevent these countries becoming first world/that it will interrupt their growth. I'm saying even without climate change they won't become first world. Certainly not on the timescale suggested. Now I agree, climate change won't help. But the reason CAR isn't (now or in 50 years) a first world country is not down to climate change, its because they don't have any of the myriad things needed to support that type of economy.
Climate change is going to cause hardship, and aren't people going to respond? People respond to changing conditions all the time. In responding to change won't that cause economic activity? Where I live there are many flood relief schemes that have an overall budget in the 100s of millions. Multiply that by all the schemes needed the world over and you have a lot of economic activity.
I know this is very close to the broken window fallacy but assuming that climate is a gradual process and not a cataclysmic one (and there's no evidence that it is) then mere capital will be deployed or destroyed and deployed. Humans can rebuild their capital. Sure, if it wasn't for climate change that capital would have been invested elsewhere but we're not talking about all capital everywhere. I think it extremely unlikely that the effects of climate change will put the breaks on human progress. However I do think it very possible that climate alarmists might cause policies to be put into place that would put the breaks on human progress.
It'd be nice if we could come back here in a generation, in 2050 say, and see what the near-term outcomes were.