If there's an approach to model imho it's the Norwegian one: Actually backed by stocks, but managed and distributed by a central investment fund. It's far easier if the country is smart enough to centralize oil profits as well though...
You just need to have a tiny population and be the 3rd biggest gas and 5th biggest oil exporter, easy peasy
That's the part that causes friction, because (soon to be) pensioners don't want to accept lower pensions, and they still have voting rights, voting in politicians that cater to pensioners over workers.
That's what Norway does too, just less directly. The $1.75T that Norway has in their sovereign wealth fund is just a claim on future output. Germany's taxes are a claim on future output.
Or to look at it at a micro perspective. Suppose you have $10M saved for retirement, but need to hire a personal care nurse. But there aren't any and you get in a bidding war with someone who has saved $100M.
The problem is the baby boomer generation transformed it to the point retirement was "when you started living your real life". People being retired perfectly healthy for more time than what they worked is not an exception for them.
And that generation managed to pile more shit on the next generations: regulations to make housing more expensive, requiring more education for every job meaning people start working later, outsourcing has much as possible. And not having replacement level children.
So now people have to pay a lot more for those privileged generations. Meaning they have less available money to get a stable situation, meaning even less children so the problem will go worse and worse. At least one generation will have to be sacrificed to have a chance for ones after them. Will the Millenials accept to be it, or will they pull a boomer?
PAYGO-style is definitly the more sustainable approach.