Raising the standard of living for the poorest people in the world does very little to increase the rate of climate change since these people have very little impact on the environment and consume so little in the first place. I'd argue that we also owe it to them because the poor are also least capable to handle the consequences of climate change and the other issues facing developing nations. I don't know why this needs to be said but those are real issues.

The flaw in Elysium is moral and practical. You have to accept that humans by virtue of being human deserve some consideration, and the well being of society deserves consideration. If a rich person don't believe this then they are irresponsible. Too much inequality in society makes it shittier for everybody for plenty of reasons.