The secret to pensions is making contributions. Places like New York that legally require full contributions are doing fine (although that is not cheap to do). Places like Illinois who skip the bill or most companies post 1980 who steal the money are a different story.

> Considering the extremely poor state of private defined benefit pension funds

The poorly funded ones make the news, but there are many healthy ones that don't. It isn't agency risk that causes problems, it's a combination of increased longevity and low interest rates.

A big problem with 401Ks is predatory investment advice. "Advisors" channel money into high-fee funds and commissionable investments and often "churn" money to generate additional commissions. The Obama administration cracked down by instituting a "Fiduciary" standard for retirement funds, but Trump has delayed implementation of the rule twice.

Almost every state and local government agency is underfunded, many in the billions of dollars. The reasoning is that they can always just raise future taxes, which allows for huge agency risk of politicians buying union votes. The politician gets elected, the current union members get paid, and the future taxpayers and union members who aren't voting get shafted.

401ks aren't perfect, but it's better than the above system. There's a reason no one sells annuities even close to what the government offers in it's pension benefits. It's ridiculously costly without using funny numbers.