Also, punishments should be amplified by the inverse of the recovery rate (basically, the rate at which that crime is solved), with the extra compensation going to a victims' fund to pay those for whom no suspect is ever caught.

I like this idea in principle, but it seems like it'd be pretty impossible to make work in practice.... would victims of crimes where no suspect is ever caught have to go to court to prove that they had actually been the victim of the crime? If so, how would that work? A trial with a John Doe defendant? And if not, wouldn't it massively incentivize people to file false police reports claiming victimhood?