Not a lot of time, and this is probably my last post today.
Incapacitation isn't the single driving motivation for imprisonment; it may in fact just be a side benefit in many cases, but I was trying to point out that it applied to many if not most crimes, and contradicted your assertion that prison is worthless. I usually see such statements unaccompanied by supporting data, or at best by data that is of highly dubious validity, so they usually raise my antennae.
Punishment has other motivations than incapacitation, but theoretically at least other methods than imprisonment could satisfy those motivations. We could impose sharia instead, I suppose, to satisfy motives like vengeance for the victim, deterrence for society, and penance for the perp. I think we've arrived at prison because of a combination of : it can (in theory) be imposed equally on everyone, it is viewed as more humane than flogging, and it (theoretically) allows for training and rehabilitation. Deterrence, training, and rehabilitation don't happen as predictably as we would like, but in my view it's wrong to pooh-pooh them, or the idea that they are partial outcomes of a necessarily imperfect system.
I have no idea what the half-lives of different criminal impulses are. They do decay somewhat with age; I think that has been recognized. But I am not in favor of a formal buy-out option.
First, a buy-out, even if you make the rich pay more, offers them a choice that the poor don't have. If you make the scale such that the poor can afford it, you may be only giving them more incentive to commit crime when they get out.
Second, you'd have to prove when sentences exceeded the incapacitation motive. How do you know that most sentences aren't less than would be suggested by the incapacitation motive?
Lastly, I think that informally, judges can take willingness and/or ability to make restitution into account in sentencing at least sometimes. Fritz would know for sure of course. And civil actions can at still accomplish your idea of making rich people pay more, without letting them buy out their criminal penalties.
Sorry, I don't have time to do better right now.