In a world with an FAI Singleton, actions that would violate another individual's rights might be simply unavailable, making the concept of a legal/justice system obsolete.

In other scenarios, uploading/splitting would still take resources, which might be better used than in absorbing a criminal punishment. A legal/justice system could apply punishments to multiple instances of the criminal, and could be powerful enough to likely track them down.

If I had criminal intentions, I would upload myself just before the criminal act, so that the upload would be innocent

I am not convinced that the upload would be innocent. Maybe, if the upload was rolled back to before the criminal intentions. Any attempt by the upload to profit from the crime would definitely make it complicit.

Criminal punishment could also take the form of torture, effective if the would be criminal fears any of its instances being tortured, even if some are not.