IMO and IME the person who has just put their stuff on the item belt is the one who should put the divider down behind their items.
Honestly I'm kinda shocked that there are places where you don't do that (not THAT shocked but, I find it weird).
And I don't get the issue with being offended.. we aren't offended. Those ARE your items and these ARE my items, we pay for our own stuff, thus the divider is needed
nothing offensive there.
And all that aside, everywhere I've ever shopped, the divider is just easier for the person in front to reach. The very few times the person doesn't put it down I feel pretty irritated at them because I have to reach in front of them awkwardly and halfway across the item belt to reach a divider, as they're usually not pushed all the way down to the end of the belt.
And if I'm not long enough to reach it, I have to stand around and wait for the person to move ahead so I can get closer to the dividers, which in turn means that the people behind me also have to wait longer to place their stuff on the belt.
It's just all around really annoying when people don't put it down after their items.