The demographics of the world mean that social security and government pensions are no longer going to work very well. They will need to be cut, and can certainly not be raised even higher. In your lifetime, most countries will have 1 worker per retiree. Some, like South Korea, will have two retirees per worker. Good luck paying all your normal taxes as well as increased levels of medicare and social security all on one income.
Investment will continue to be the cornerstorne or retirement, the math for redistribution just doesn't work. Especially if you increase the distributions.
The government can invest just as well as individuals can. The only difference is that everyone would get the average growth, rather than the wise or lucky getting more and the foolish or unlucky getting less. If we can't afford to fund people's retirement that way, they can't afford to fund it themselves either, and investment accounts were only ever about shifting the blame.
Investment will continue to be the cornerstorne or retirement, the math for redistribution just doesn't work. Especially if you increase the distributions.