As an employee benefits lawyer with 40 years in the industry, I think there is zero chance that 401(k)s will be eliminated. However, there is a lot of incorrect information your post.
Many state and local governments have switched to defined contribution programs for ongoing pension contributions, and their defined benefit plans have been frozen or allow contributions for a grandfathered group of employees aging out of the work force. And some of those entities use the governmental version of a 401(k), the 457(b) or, for teachers, the 403(b).
Union employees working for private companies also pay into social security, as do some governmental employees.
Pension plans for union employees working for private employers do not have an employer match, and the level of contribution is controlled by the collective bargaining agreement. They do not tend to be generous as compared to the limits for 401(k) plans.
As for investments, I am part of a large group of attorneys at my firm that handle the legal aspects of investments for government and multiemployer plans covering union employees of private employers. While those plans purchase annuities and guaranteed investment contracts, most of our work involves investing assets in private equity funds, private real estate funds, individual real estate investments (debt and equity) and other alternative investments. These plans also tend to have large investments in publicly traded stocks and bonds.
Private employers don't bail out troubled union pension plans because the members beg them to. They don't pay any more than required by the collective bargaining agreement, their subscription agreement with the plan, and the relevant law. I agree that taxpayers can end up getting a raw deal when public pension plans are underfunded.