You still have the problem where crime X (let's say stealing a car) and crime Y (maybe shooting someone in the leg) result in the same prison term, when normal people would say that one of the crimes is a lot worse. Prison plus fine is barely multidimensional, and converting prison to money reduces it to one dimension again.

In a study like the one you propose, they should also see what effect the crime causing the prison term has on the valuations - will time in prison for rape cost more or less than time in prison for murder?

In my opinion the justice system should aim to convert criminals into productive members of society, and protect the rest of society from said criminals until they're fit for society again.

Since it's not a simple problem to solve, I don't have a better solution than "use common sense and take as many aspects as possible into consideration, and dont' forget to look at the big picture". Saying that money is the only thing that we can measure and so it has to be the basis of any decision is to pretend that it's a simple problem.