Earlier quoted context omitted.
We aren't heading to extinction just on account of birthrates, it's the transition phase with a large number of elderly dependents and a small number of workers that is going to be the real problem.
Unless most work is intellectual/creative and most manual labor is automated or machine assisted 50 years from now. There are way more 70+ year olds still in the workforce currently than ever before and it isn't crazy to think retiring at 60 is a thing of the past.
We are also seeing a trend where technology is leading to additional surveillance and control for the population as opposed to a reduction in inequality and rising living standards.