Leno and Kevin Eubanks had some great chemistry but yeah, it was mainly just for jokes and punch-lines during the opening monologue and some occasional bits. Conan is in a league of his own, he and Max Weinberg and then eventually the rest of the band and then eventually his entire staff from his assistant to Pierre Bernard to Jordan Schlansky to etc, etc, he really uses his whole crew and frequently too. They're some of his best bits. Fallon and the Roots do tons of bits together, from thank you notes to slow-jamming the news to family feud to etc, etc, they're a big part of his show too. Kimmel doesn't really use his band that frequently I find. It's just mainly his staffers.
Letterman, James Corden, Craig Ferguson and Seth Meyers I don't/didn't really watch much of so I can't really comment. I guess it really does vary from show to show, but the shows that play to their band/staffer personalities really shine I think.