I strongly dislike that definition of the state. Such a state as described in the pithy phrase has never actually existed. Even the very strongest states have

I strongly dislike that definition of the state. Such a state as described in the pithy phrase has never actually existed. Even the very strongest states have violence that the state was powerless to stop. That objection can only be resolved by reducing the strength of the term "monopoly" to something more like plurality control, but then it does apply to power in general. Simply put, if some other coalition has more general power than the state, then it has the option to become the de-facto state. There are lots of terms for this, depending on the party with the power: from revolt and coup to occupation to ineffective government. There's a discussion to be had about how to best allocate that plurality control to minimize abuse, and physical force is likely a component of such an allocation. It's far from clear, however, that an allocation of only physical force is viable even if it is desirable.