But wouldn’t productivity increases due to roboticization, automation and AI take care of that problem?
China has been automating its economy, for that reason.
Can a fully automated economy support the people within that economy?
Automation can help as can productivity increases but its not enough to offset the effect of aging. It makes the loss of productivity due to aging not as bad as it otherwise would have been, but it still has a big effect. For example, in 1990, Japan had a GDP per capita higher than the US ie $26,345 vs $23,840. Today US GDP per capita is $95,210 and Japan's is $35,400. Japanese workers did not become less productive. Japan just aged much faster than the US. Japan's dependency ratio increased a lot.