One additional assumption: there is no significant target shift.
Armed robbery for taking week's profit from ten businessmen may be less of a strike to all of them in sum than armed robbery taking months' salary from a minimal-wage-working single mother. It would count for a greater crime rate, though...
If all this were true and if the model held around zero, then doing the thing that minimizes suffering would be good.
That doesn't mean we should not check if other forms of punishment would drop crime rate further.
Of course, the model would have to include a lot of stability checks. With 1¢ fine for every crime, people would use a lot of interesting weapons for self-defense in broad sense (including defending good neighbour's property from theft by force just in case). People wanting retribution would do the retribution themselves... Some other interesting effects would occur...
If that worked out to lower aggregate crime rate for each victim group - it would be nice...
Here is a thought experiment for you. There will be some bold assumptions here, and they may be regarded unrealistic. I am aware of that and the purpose of this query is not to propose some truths about society in general, but to isolate certain characteristics of preferences regarding the societal institutions of law enforcement and punishment.
Assume that there existed a highly trustworthy model that showed beyond reasonable doubt that crime rates anti-correlated with harshness of punishments imposed on criminals. So basically, if policies changed towards shorter sentences, lower fines and lighter penalties, the number of criminal acts decreased (in every category).
Further assume that this was empirically tested and each time penalties went down, fewer and fewer crimes was committed. But the dependence was not linear so if we would get rid of punishments all together - there would still be murders, rapes, robberies etc. But, the crime rates would be minimized in that case. To summarize: We knew that crime rates would be at minimum if there was no consequences at all.
With no penalties, somebody could simply kill or rape your mother, sister or child and move in next door and live a nice and happy life in front of your very eyes, without society doing anything about it! Bare in mind now that this is the situation where the probability of your mother, sister or child being abused, robbed or killed is minimized!
Would it be reasonable to go trough with this demobilization that would spare lots of innocent people all the pain of getting robbed and abused, given that those criminals still out there can do anything they want and go free?