It took a much shorter time to watch the Seth sequence play out than it did to read my analysis of it. However, it was an important and highly memorable scene.
The impact was necessary, even if we did have to rush through twenty-one different (and strategically unrealistic) time-lines to see it as a linear plot. Seth's sub-plot helps to underline the options open to Joe during the second part of the movie.
Some of these are actually used. For example, cutting yourself in the present day will leave your older self with a scar. Seth was left with an address etched into his arm, so was Joe.
Dismemberment, in any form, will result in your older self similarly being dismembered.
The Seth story raises a huge question - why didn't the Gatmen just kill the younger Seth, instead of mutilating him?
That's answered in Joe's second time-line. Because a looper's untimely death will result in the older, retired looper ceasing to exist too.
The time-line would just erase itself and place both Seths back into the courtyard at the execution scene. We would then be caught in a vicious causality cycle each lasting just a few hours. Seth runs; his younger self is killed. Seth runs; his younger self is killed. Seth runs, and so on.
Even in 2072, time-travel isn't an exact science. It was immediately out-lawed. Maybe nobody knows what would happen if the flexibility of time was so abused. Maybe they are too scared of the potential issues to find out.
Also the loop wouldn't be cleanly closed (according to the rules of the mob, not Physics now); and a bone fide murderer would have been created. Someone would have to kill the young looper, whose birth has been registered and who exists in that time-line.
Remember, until now, the victims are from the future, hence they don't necessarily exist in the past. Therefore their murder can't be prosecuted as murder. No official existence, no crime. Those making the rules are in the future, where killing is very problematic. They are making rules to deal with issues which similarly don't yet exist in the past.
Despite their jobs as assassins, the gangsters don't like to have murders on their hands which could possibly be treated as such by the courts.