It should be possible to do that seamlessly as an ESOP ~ however the federal government would lose about 50% of the value added per year to the federal retirement annuity "funds" and would run an even higher deficit.
government worker pensions need to go along with the privatization.
As I recall, ESOPs were a precursor to 401Ks, is that what you are talking about? I forget how they worked, but I don’t remember them being particularly beneficial.
All that I remember about them is that you couldn’t roll over dividends in them and when they were changed to a 401K, they never allowed us to roll over the dividends.