Earlier quoted context omitted.
You cannot ultimately chain people to their desks. What you either get is a "soft" withdrawal of labour (people refuse to take the job if they have any other choice available, as we're discussing upthread, so you get dregs), or the whole thing explodes into "illegal" strikes. Which are harder to resolve, because you made sure there's no one organisation to negotiate with.
the US has at-will employment, save it with the hyperbole. There are plenty of non-unionized jobs people would love to have. Collective bargaining against private actors is fine. There should be no collective bargaining against the democratic will of the people, any more than some random group of federal workers has veto power over law passed bu congress. It is simply not how democracy works.
Presumably this also rules out any company or non-profit from negotiating a contract with the government, or suing the state.