The private sector doesn't have a monopoly on violence that it can use to imprison me.

It doesn't have a monopoly, true, but the private sector can and does engage in violence and imprison people.

Does that matter in practice? Large private-sector entities can employ organised criminals to assassinate you. Pragmatically, how is that any different? Dead is dead.

At least with the government, you (theoretically) have due process. True, the Constitution (or equivalent documents in other countries) is worthless if not enforced and observed, but the private sector has no such guarantees.