PAYGO vs investment earnings is purely a financial construct.

The central issue is that physical goods and services need to be produced around the time that they're consumed, and at a given point in time, an economy has a fixed capacity to generate these goods and services.

If you have a non-producing population, and a producing population, then the only way for the non-producing population to consume a given quantity of goods and services is for the producing population to not consume those goods and services. Whether you call the reduction in consumption ability of the working population "taxes" or "investments" doesn't change this fundamental fact, except insofar as it alters certain behavioral incentives around deferring consumption and legal frameworks around property rights.

(This isn't 100% of the story, since you can "lay claim" to production of working people overseas via international investment, but is accurate in broad strokes.)

Since you said capacity is fixed _at a given point in time_, this is technically true but not really useful.

Populating aging happens over time, not all at once. Overall production also changes over time. It’s not inherently true that for “non-producing” (not sure exactly how you’d define that) people to consume goods the “producing” people must consume less, at least not relative to past levels of consumption.

You're right, it's not necessarily true relative to past levels of consumption. But there's a limit to economic growth, and the choice of "paygo" vs "investment" probably only has marginal effects on the rate of economic growth, so the point stands.

"Non-producing" people are retirees (as well as children). People who don't produce market goods/services that make up the vast bulk of our material needs.

> If you have a non-producing population, and a producing population

Isn't this true of capitalism generally, and not just for retirees and young workers?

The "non-producing population" is commonly called "capital", and the "producing population" is commonly called "labor".

On a macroeconomic scale it is still the workers paying for the retirees. Doesn't matter how many millions you have in the bank if there aren't working people you can trade your money for goods and services with.