How would you qualify the "right" in the above? Would you say that it has to be a natural right, but not necessarily an unalienable (in your narrow sense) right? I would think that you would; otherwise you need to explain to me why the ability to rescind the right has such a determinative logical connection to the just powers of government.
I don't view it as a right. Like overthrowing a tyrannical government, punishing crimes is not so much a right that exists as an option as it is the right thing to do, a moral duty (in fact, overthrowing a tyranny is a subset of the larger duty). And I don't think it's alienated at all. Who would carry out a necessary revolution, if not ordinary citizens?
I think my way avoids your choice altogether. The government ought to punish crimes as best it can, and so should citizens. That may mean turning suspects over to the police, but then again, it may not. Neither are free to determine for themselves what constitutes a crime. Any violation of life, liberty, and property is a crime, including punishments inflicted for a fake "crime".
That is the second alternative: "the government picks and chooses which rights to enforce", - in other words, which rights violations should be treated criminally.
Why would I have to say on behalf on individuals?
You describe a system where the government just is, handed down from history, and acting not on citizens' behalf but because it chooses to, like a dragon in a castle. You then draw a distinction between good government and bad government, and you say that bad governments ought to be overturned. I assume they ought to be replaced with good, or better, governments. Two questions arise:
1. Is there an objective way to tell good government from bad government or is it something the citizenry determines implicitly as it goes through elections and revolutions?
2. How is the process of elections and revolutions, that reconstitutes the government, different from establishing a government with consent of the governed?