I think he makes them a lot better.
1. The bulls are the best percentage 3pt team in the league but lowest in attempts. They have a math problem. Their "4s" like Green and DJJ only put up 1-2 3s per game. Barnes puts up 5 and hits them at a 45% clip
2. Because Lavine, Vuc, and Demar operate so much in the mid-range, you don't want a guy that also needs to play there. Barnes would be fine just hanging and getting easy corner 3s. Barnes basically shoots 3s or close 2s. And he CAN back a guy down if needed, which is helpful in the 2nd unit.
3. He is not a great defensive player but he has often guarded the best offensive player on the opposing team and been neutral, and that is on a very stupid defensive team in the kings. The Bulls WITH caruso and ball are actually quite smart on defense, and it's believable he'd do the same.
4. He gets to the line 5 times per game, the guys he is replacing do not get there consistently
He's a bit like our discussions of Jeff McNeil for the sox. He's not the greatest player in the world but his strengths fit nearly all of the white sox weaknesses (LH, Low K, Strong OBP, Strong Defense).