Paying with time is bad. If you pay with money, and the other person keeps the money. You pay with time, and it's gone. We are all poorer for it – you are poorer the same amount, on net (if equilibrium models of how people queue are directionally correct), but the shopkeeper gets nothing.
For instance, if you fix a price lower than it would normally be, it makes sense for a lot more people to want it. Typically, those people just wait for their turn to get whatever it is they want, and the equilibrium wait will be when it wastes about as much time as the price controlled discount. This is what people saw in both the Soviet Union and in the lines for gas in America.
So why do we ask people to pay their debt to society in this deeply wasteful way? I suspect it is because the degradation is seen as a useful deterrent, but I'm sceptical that, even if it were effective, the moral calculus would work. There is a reason we don't execute everyone we incarcerate, and it's (at least partially) because it would be a tremendous waste of human life. Incarceration is just a fractional wasting of the same life.
I'm concerned, in general, about humans in cages. That's not where we belong. Not ever. Sometimes we need to exile horrible criminals, to have them not be in society. But the reason it's used as punishment is because it attacks our dignity so directly. It is a pure cost to humanity, a degradation. I don't think it's crazy to think that, there must be a better way, aside from having them wait in cages.
They say time is money. Why have someone in a cage when they could be useful to us? I think the free market is the best way to get the most valuable use of out them (and almost anything would rehabilitate more than the current system), so they need to be able to interact with it, with their incentives essentially intact (that's right, no weird prison slavery, that won't help anyone do anything).
To be clear about my proposal: Perhaps we should replace medium-length prison sentences with a big fine, payable to the victim of crimes, and a flat N% tax on all future earnings (possibly limited to 10-20 years).
To answer the obvious questions: serious crimes, such as murder, violent rape, slavery, or torture, deserve relatively limited forgiveness. We should all be extremely cautious of any non-life-ruining punishment for crimes worthy of deep disgust. There should be some mechanism for forgiveness, but I have no clue what that ought to be.
Honestly, if you (like me) are not super comfortable with murderers walking free, why would it matter if they spent 20 years in jail in the meantime? There is little reason to think our current system changes them. There are deeper questions about what justice demands, and what societal order demands, and how those aren't identical. I'm just ignoring all of those hard questions because I'm not sure the answers exist or are even taken into account in our current system.
I think it's becoming clear how much fines and pretrial monitoring can replace jail – quite a lot, it seems to me. But we should all take this moment to also consider, to what extent fines and taxes could replace prison as well. What do we want from the justice system?