Imagine a future where there are half as many the workers as retirees. It doesn't matter how much money retirees have in their pensions if they cannot hire workers to look after them (do their healthcare, produce the food they eat etc). You'd just get rampant inflation as the richer retirees competed to get workers, and everyone else goes without. In other words, in that scenario the value of the saved money would be eroded by inflation.
Now I will admit that this is complicated by there being other countries, or if we invent humanoid healthcare robots or whatever. But there's a principle involved that someone (/ thing) has to do the work.
Yes, and that's why this basic pension can only be something guaranteed by the state. In case of war or massive devaluation or change or currency, the state (maybe not even the same one under which "rights" were acquired) can guarantee these things (and will want to guarantee them, in order to preserve the pensioners from poverty).
It's debatable whether paying into your own account is a transfer of wealth at all, even if you're not able to withdraw your money until retirement.