You can't have a proper pension system if you don't have enough young and middle-aged workers to pay for it, and to work all the jobs necessary to keep a society running.
you can, you can have your pension in savings investments without anyone's else financial contribution
it's just that most of the world is using archaic thorough/continuous model for pension system which is basically pyramid scheme everyone would avoid if it were used in any other area, but somehow is acceptable for pensions
if you really worry about pensions, you could start with children contributing to their parents pension and nobody contributing to childless people, that should solve declining population very fast, your can combine it with raising retirement age and raising fees everyone pays towards their own retirement
On a national scale, private retirement savings are not that different from pensions. Both are based on tokens that entitle you to some fraction of the economic output of those who do productive work. The value of a token depends on the total number of tokens, the size of the real economy, and the fraction of value the people doing productive work are willing to pay as taxes to the government and the capitalists.
Investing internationally changes some things. Retirees bring in money from abroad, but that does not increase domestic production. Prices will go up, as there is more money competing for the same goods and services. The people doing productive work will want more money for their services. Imports will be relatively cheaper, but the economy suffers, because the exports will be less competitive due to higher wages.
Saving for retirement is rational for any individual if the demographic structure cannot support the pension system. But while anyone can do it successfully, it's not possible for everyone at the same time.
> you can have your pension in savings investments without anyone's else financial contribution
Those investments still need workers to work in the underlying companies, and that doesn't count products that don't usually get covered by pension income e.g. healthcare. Those investments _will_ go into terminal decline if the labour and demand provided by the non-retired starts collapsing.
