The entire concept of the Loopers just seems awfully silly and contrived, with mobsters using time travel technology and setting up this entire, complicated system.... just to off people?!? (Really? Because they don't have incinerators in the future or something??)
Supposedly, they have 100% perfect tracking and biomonitering implants in the future. If you kill someone the police will know exactly when they died and who was there with them. That means that the identity of the killer will be pretty obvious.
Sending them back in time means that they vanish from the tracking system, but there is no death signal.