Whether or not there are enough young people does not matter.

The plan was to have fully funded pensions, bootstrapping them after the start. You cannot have infinite growth any case, as eventually we run out of space and resources. It must come to end at some decade.

However funding pensions full was never executed. It was too easy for politicians not to pass taxes, social benefit costs and such to do this, because boomers would have complained decades ago when they were still in the fullest earning potential.

So it does matter. Contracting economy, aging population, worse social dynamisc, political and institutional inertia, productivity drops, etc. Robots aren't going to offset but a tiny part of this.

And between payroll taxes and the fact that stocks, 401ks, etc depend on economic growth, things will turn real shitty...