Economic hot take: That scale of saving is impossible. It can't happen. The ends don't meet, the numbers don't match up.
Think about what etiremnent savings means in the real economy. It means I have to store enough food to feed myself for 30 years. It means I have to store enough furniture too. And enough gasoline. And enough of everything else.
This is obviously not possible. So instead I store other things I hope I'll be able to exchange for gasoline and food. But no matter what form it takes, I have to store an absolutely enormous amount of stuff. Whether it's physical goods or abstract financial rights. There is no way for everyone to do this without creating massive economic distortion of some kind. Whatever people store is going to massively increase in value (house deeds! shares!) and crash later when they exchange it for food and gasoline.
But there's a simple alternative, we add a 20% tax and distribute it to people in the form of pensions. This is called a pay-as-you-go pension scheme. Optionally the scheme can keep some kind of weight value for each person based on how much tax they paid or any other metric. Since it doesn't store assets it doesn't distort the economy nearly as much. But, it's vulnerable to a future generation simply cutting it off. When the scheme turns on there's a generation who didn't contribute but still benefit and when the scheme turns off there's a generation who contributed and didn't benefit. This can't happen to people who store real assets because the assets are firmly owned by them, and the society can't easily just decide they aren't.
We can do an intermediate solution if we let people buy a share of future tax income as a financial asset. It doesn't distort the economy too much and your contributions are firmly your property. Treasury bonds are this.