Didn't see one created already, if there is one already please delete.
I found this Rain Johnson interview
from 2012 that tries to explain some of the mechanic/mysteries of the movie.
One in particular reveals his thoughts behind the "closing your own loop" requirement:
6. Why is it essential for a looper to close his own loop?
This is another one of those questions Johnson had answered in his head but didn’t put in the movie. In fact, he even conceived a scene with Abe addressing it but never shot it.
“People in the future, all they know about time travel is to be afraid of it. So they’re trying to keep it as tight as possible. So the initial reason they set it up this way was to keep the causality loop as tight as possible,” Johnson said. Because, for example, if someone else kills your older self and you have to exist with your own murderer for 30 years, what’s stopping you for murdering them or doing something to screw everything else up? “Every bit of evidence is gone from that loop when you kill yourself,” he said.