The only thing that can work (which is also what is happening in practice) is to continually adjust the “pension & welfare” age upwards to achieve the necessary balance between working years and retirement years.
The upshot is that everyone will need to save more for retirement than they do currently, whether privately or via taxation.
Well, that's what seems to be happening at least in Germany where I am. Retirement age goes up, retirement benefits (inflation-adjustment) go down, contributions to pension system go up.
It's always a bit of political struggle of course with back and forth, but the general trend is just that.
Nobody likes paying more and getting less, and it’s perceived as some kind of societal decline, but it’s more like a correction. I don’t think it’s a coincidence that the high birth rates in developed nations declined, roughly, in conjunction with the rise of welfare states. Both are ways, roughly, of providing for yourself in the future. Both are unsustainable in their current forms.
We are living in the age of peak entitlement, where we draw down on the finite fossil fuel reserves of the past while simultaneously drawing down on the earnings of our children in the future.
This is the same thing. Human lifespan can't extend indefinitely, so if you continually adjust retirement age upward, eventually you adjust it to a point that nobody ever lives long enough to retire.
The upshot is that everyone will need to save more for retirement than they do currently, whether privately or via taxation.