You have perhaps missed my answer, that was also addressed to this. It may be worth repeating. Financial savings are an accounting fiction, that cannot shift any real resource into the future.
The pool of available resources at a given moment: food, housing, infrastructure, human labour, raw materials, is what it is. Financial "savings" do not shift it in time, do not magically expand it. If people save money (or any other form of financial asset) and then all decide to spend savings on resources, the resource pool remains the same. All you get is inflation, and those savings being show as an illusion. And when talking about a social security scheme, how it's sustainable, it's the macro level that is being discussed. This was what I addressed originally. "Capitalization" for social security is a financial scam.
Because, and pardon me laboring more on this, in terms of real resource use a social security system must always balance on the present.
Personal savings may work for you individually if and only if you save more than the others. In that you will later outspend those others in bidding for limited recurses. But collectively - this is a social security system we were discussing - it's a zero-sum game. Look at you example:
You talk about retirees consuming resources. To meet their need for resources, the people in active labour pool must produce those resources at the same time they're consumed. The system must balance. Whether the laborers are "taxed" and those taxes "pay" for the pensions, or the retirees spend "savings" and but resources in the market, the end result would be the same: a fraction of the resources gets spent on retirees. It's just two different ways to organize the transfer of real resources from laborers to retirees going on in the present. Because the vacations you didn't consume 20 years ago are not frozen in time waiting for you in retirement: the workers of your younger age who would have served you have also aged and are also retirees now.
Thus pay-as-you-go versus capitalization is a matter of formal organization about the transfer or resources in the present from laborers to retirees.
What I am arguing is that pay-as-you go is superior for two main, very important, reasons:
1. It more accurately represents reality, preventing fallacious presentations like saving for the future. All transfers of resources happen in the present and are a choice that present society must make. This is always true, it's a material reality. A system that more plainly shows that is superior.
2. Capitalization provides more opportunities to useless rentiers to peddle complex financial structures and siphon off a share of the "financial flows" for their own luxury consumption. Seize a share of the resources for themselves as "necessary specialized service providers" of finance by pretending they're providing supposedly necessary "financial services". Which are always much more bureaucratic and obfuscated than the pay-as-you-go state administered systems.
Capitalization is a system exploited by a parasite class. That is why banksters keep pushing capitalization and trying to cancel pay-as-you-go. A more obfuscated system gives them opportunities to present themselves as necessary middlemen and organizers. They're not - they're social parasites.