I agree: I fear an oppressive government more than anything else... but, I also fear an ineffective one where might makes right.

There is a delicate balance and I believe that those who cannot be rehabilitated have no place in any of the state-society blends: they only have a place where might makes right.

When the state can freely decide whom is bad it gains more power. When there is no "life in prison without the possibility of parole" as an option then the people (e.g. the jury) are the ones that make the decision on whom lives, whom dies and whom gets exiled.

The state "should" be subordinate to society, but it is also an independent entity that tries to act on society. There is a conflict. Society must remain vigilant against its own state. I think one of the important lines we must draw is how the state may deal with people it deems undesirable. There is no law allowing exile or execution that has not been abused by individuals with power within the state apparatus. Nearly all the great human atrocities in history have been committed in the name of a state. I do not believe the state should be allowed to accumulate so much power. I would rather have an impotent state that has difficulty keeping people behind bars than a powerful state that has no difficulty killing people. The state is not society's only or best tool.

Distinctly possible.
I don't see society as a thing that has a purpose: it is the evolved aggregate behavior of the masses. That is why there are different social customs in different populations - because the customs evolve out of the congregation of people.
The state, however, is a creation of the masses to try and manage society in a way that benefits all those who are members of the society.

If looked at from this point of view then there is no benefit to society or to the state for supporting those who cannot be rehabilitated and released into society.

I think you and I have different ideas about what the state and society are for.

That's a low enough chance that we take it most other places...... even when lives are at stake.

So exile them.
The point it: if they cannot be a productive member of society then society should not support them. Let them wander into the wilds of Alaska and, if they can, support themselves away from everyone else.
Start a permanent moon base with criminals (yes, the new botany bay) and let them go there to work on the construction.
Whatever - just don't make the rest of society pay for they who cannot play nice in society to live without contributing to it.

Because the state shouldn't have the right to kill an unarmed, restrained human under any circumstances.

Thing is, you're wrong about 5% of the time.

I think their lives serve no purpose so why support them?

It's only money. I suppose you think lives are cheaper?