Pension plans and 401K/IRA are invested in the same thing.

The only difference is a pension plan board/fund manager is an additional middleman that can be stupid/corrupted, hence more agency risk for the benefit recipient.

Taxpayer funded pension plans offset that agency risk with the power of being able to increase taxes, assuming their tax base is sufficient.

Historically, many pensions were defined benefit, rather than defined contribution. Market risk (and benefit) fell upon the employer rather than the employee. My understanding is that defined benefit pensions are pretty rare these days.

The problem of pension is that it doesn't come out of thing air. Someone still has to pay for it. In US the company pension get raided. In France pension is gonna run out soon and it put much pressure on the young people. Unless you have deep pocket like Norway oil money, pension would always favor the old. I have never seen a pension system that favors young people instead of the old yet. I think 401k style of you get what you pay is at least fairer to the individuals.

I remember Bush got a lot of flak in the press over his attempts at partial privatization of Social Security, with a payroll tax going into named accounts invested in broad-based equity indexes. (The details differ substantially, but it was somewhat like making 401(k) contributions mandatory and deducted from every paycheck.)

Increasing the size of the investing class and putting names and yearly balance statements on accounts (so voters will call bloody murder if the legislature raids the funds like they currently do with Social Security) both seem extremely useful to me.

Though, increased transparency would likely force reductions in benefits for current retirees, with current workers being the beneficiaries. Also flooding so much money into the major indexes would likely bring down investment returns, but likely resulting in a slight narrowing of income inequality.

And the risk of the employer not existing or being profitable enough decades in the future still falls on the benefit recipient, so just another agency risk.