The traditional pension systems (defined benefit programs) have turned out to be very vulnerable to insolvency. Hence the transition to defined contribution programs, like 401ks and IRAs.
SS is a defined benefit program. Its insolvency is a problem with all such systems, including the ones you advocate for.
Traditional pension plans should work better than individual retirement investments because they pool participants. Individuals have to invest enough to get the payout for their longest reasonable life expectancy. A pension fund can rely on statistics and not be funded enough for every participant to live the longest time.
Emphasis on the word should. Humans are bad at managing huge amounts of money.
private pensions are typically not adjusted for inflation. you're trading a slice of an uncertain economy for a guaranteed amount of an uncertain currency. pensions could be inflation-adjusted, but then you have to trust that the official inflation figures actually track your personal expenses. it's a tradeoff either way; no one can guarantee that there will be enough surplus to support the non-working population several decades in the future. but at least 401k upside is uncapped.
> Traditional pension plans should work better than individual retirement investments because they pool participants
I don't see any particular reason why they would. Lots of individuals do much better with their investments than bureaucrats do. Also, there are many "fire and forget" index funds available for those with little investment skill.
Defined contribution plans have been an abject failure.
Quite simply, the guise of individual exceptionalism and the illusion of financial control was used to justify the shift away from pensions, which shareholders took profit from what would’ve been pension contributions, and compounded by stagnant wages, a substantial amount of workers were left with nothing.
SS is a defined benefit program. Its insolvency is a problem with all such systems, including the ones you advocate for.