There is a difference though. The pension based on the pay-as-you-go system on wages and salaries, as we have it now, can only draw its benefits from wages and salaries in Germany. This is a problem in several ways: First, the demographics are worsening, instead of 2 or 3 workers per retiree, the ratio will soon be reversed. And second, it only relates to labor, but there are other factors of production. Currently important is especially automation, i.e., capital. Third, the levy is applied to all labor, regardless of whether the company in question is on the verge of bankruptcy or making record profits.
A funded capital system also very easily allows tapping into the other factors. Capital returns are mainly generated in profitable sectors. Capital returns can also be generated outside Germany. In the economy of industrialized countries, the capital factor dominates. But we are still doing social policy like decades ago when labor dominated, partly due to favorable demographics. Of course, this could now be regulated via tax subsidies, but the problem is that in practice taxes are easiest to collect from the middle class and hardest from international corporations. Capital returns can very easily be collected from these via the stock market.
It is not an either-or but a both-and. Some countries recognized this ages ago and have made old-age provision stable on several pillars in the form of a statutory pay-as-you-go pension and funded capital in the form of private provision and company pensions. Here in Germany, they lack the courage to ask people for serious private provision and to give them the necessary freedom for it. Here private provision was rather seen as a job creation measure for insurance agents and in the end, you get 50€ Riester pension.
You describe the problem completely correctly.
You also name the solution: tapping into capital returns.
So sharing the profits of companies in pensions. This is possible via the stock market but only with companies that also place products there (bonds/shares). Alternative?
The problem I generally pointed out remains: demand for a company’s shares cannot be the same as demand for a company’s products. Only the latter generates the revenues from which pensions must be paid.
It is national accounting: What is saved in total by acquiring the funded pension entitlements must come into the system elsewhere as debt, otherwise it does not work. Who is supposed to take on this debt?
You simply cannot avoid a few “laws of nature” of economics.
(This is not to say that you do not have valid points. There are just often hidden side effects I want to point out).