So I don't think this is a good idea for a lot of the reasons outlined by other people. The fact that you can just stop playing the PC and let things time-out with no risk to yourself defeats the point IMO.
But also, since we're making the "real life" comparison, I think it's important to point out that "Statute of Limitations" is being incorrectly represented here in a number of ways. The concept is that crimes have a certain time in which you can "charge" someone - like, cops can't witness someone speeding and then go try to issue them a ticket for it 70 years down the road. A lot of serious crimes (like human trafficking, sexual assault, and murder) don't have a statute of limitations at all. You can charge someone 100 years after the fact and you're still good. It's different for different categories of crimes. Furthermore, it's just the time limit on STARTING legal action against a person. If you've already charged them and acquired a warrant (essentially what a bounty is, here, since you're calling for them to be apprehended), it doesn't ever time out. Just because you unlawfully evade law enforcement for a set amount of time doesn't mean you get to be "in the clear."
So the RL comparison isn't really there, even. If you break the law and get caught doing it, you can expect to live as an outcast or work it out IC. There are a lot of people who have done both of these things successfully, so don't feel discouraged.