Public sector unions are strongly against that sort of arrangement. They prefer that the taxpayer guarantee them a defined level of pension benefit (no matter what the investment markets do).

In other words, it seems that public sector unions want the taxpayer to insulate them from the real world shocks which the other 80% of people have to endure. It's a very valuable benefit and it's understandable that they fight for it. But it is super expensive for the cities and states.

In LA there was an attempt about 5 years ago to gather signatures just to put a measure on the ballot to transition city workers from defined benefit to a 401K style defined contribution pension plan.

But certain public sector unions made it known that they planned to send their people out to sign those petitions with unverifiable, fake names and addresses. This would increase the likelihood of a failed signature verification process, meaning that the petition would probably not succeed at getting the measure on the ballot. So they dropped the whole effort.