Unless I am misinformed here, there are ZERO negative consequences to not participating; the status quo is maintained. It seems the height of arrogance to me to say that they shouldn't be given this choice because (unsaid but implied) they aren't smart enough to decide for themselves. Forgive me, but who the hell do you think you are to think that you know what is best for them? Do you feel the same about programs that offer time off for working hard labor? (plenty of people choose hard labor as a career because that is what their skills are best suited for)
Should people be protected from "predatory payday loans", or should they be given the choice?
Should people not be allowed to participate in experimental drug/surgery treatments because they are desperate and dying or should they have the choice?
Should people not be allowed to quit their job and sell everything because they have an idea they think will make money? Sure, most fail, but some succeed spectacularly. Think of all the things that we wouldn't have without this freedom.
You call it "government force", but where is the force when they are given a choice and basically told absolutely nothing changes if you don't want to do this, but if you would like a free vasectomy, we will give you 30 days off your sentence?
I'll try to answer in the order asked:
1. I'm me. That's who.
2. No. Labor is not permanent. Vasectomies are. Additionally, the intent is to permanently curtail a universally recognized and constitutional human right as part of the government's punishment for what are very likely completely unrelated crimes.
3. A free market implies no government force or coercion. Few markets are completely free, so even mostly free could be considered in this category by most people. To directly answer you, yes and no to each part. People should be able to choose, but government's role should be to protect from actions that are shocking to the conscience. IOW, people should be mostly free but should be protected from the most extreme and unconscionable actions of others. Where that line is drawn can be debated elsewhere.
4. Again, should people be able to freely engage in private conduct free from government force or coercion when they may receive some benefit from a drug or other treatment and doing nothing is likely to lead to certain death? Yes. The role of the FDA should be to protect the public from unsafe drugs. Unfortunately it often does not work this way and the FDA is actually a source of many problems in this sector. There is a need for an FDA which is not always what the FDA provides. Keeping people from potentially life saving treatments when the alternative is death is unreasonable and unconscionable government force interfering with the right to life and the freedom to choose what goes into your body.
5. Again, the government should not force or coerce anyone to not choose to start a business or create art or whatever they want to do other than work a steady job. Government should remain neutral on the matter.
6. The government force occurs when a person is incarcerated and continues until the moment they are released. The coercion occurs when the offer for early release in return for a vasectomy is given. All of this occurs under duress, which is legally recognized as a condition/action that may invalidate a contract, rendering it void and unenforceable. The government is causing the duress through its force. You assume the government has pure motives in doing so in the first place. I do not. It may, at times, make a mistake or worse yet intentionally frame someone to reach this desired outcome. Case in point: recent video of cops planting drugs at a scene without realizing their camera was recording video for 30 seconds prior to the cop hitting the record button and catching himself in the act.
You are turning the argument on its head by stating that a person should be free to choose under government force, coercion, and duress. The point of freedom is to make choices that are free from government interference. You are arguing that a sort of Sophie's Choice is really what freedom is all about. It's ridiculous on its face.
EDIT: Or stated more correctly, you are arguing that the government should be free to use the force of its power to coerce detained persons to "choose" permanent sterilization under duress in exchange for a paltry reduction in their sentence for a crime not remotely related to the ensuing punishment which is cruel and unusual when this very punishment has a history of being used by this same government to advance an abusive and tyrannical agenda of eugenics intended to curb the reproduction of those deemed "unfit" and which by and large remain the largest populations incarcerated by that government - those populations being the poor, mentally ill and challenged, and minorities.
You are not arguing for individual freedom. You are arguing for more abusive government power.