I think you're vastly overestimating the simplicity.

Your 2 proposed solutions and its problems:

>The state simply pays an insurance company for an equivalent annuity.

This requires a willing insurance company that wants to be on the hook for it. The problem is no rational insurance company with competent actuarial skills would calculate that the Illinois premiums payments would be enough to meet 100% future pension obligations. Or, you'd get the alternative scenario where you have a dishonest insurance company just taking the premium payments with no intentions of paying all the pensions and conveniently declaring bankruptcy. Therefore, you'd have the same "unfunded" liability as you have right now.

>Or the state pays the union the normal cost (the cost of whatever defined benefit pension is earned in a year of work), and then it's the union's problem

Again, the union would have to agree to this. The union isn't a puppet of the state such that they would automatically agree to anything the state proposes. The union is an adversary against the state when it comes to negotiating pay and benefits. The union does not want to be on the hook for the increasing future benefits; it wants to the state to have that financial responsibility.

Your "simple" solution requires self-interested actors to do what they don't want to do.