Lots of things happen during body roll and I hadn't thought about the driver's body actually moving around but I can see that being a thing too!
One factor we think of that isn't super obvious is that there are axle steering effects that happen during one wheel bump (articulation or body roll) and leaf springs are generally pretty forgiving (compared to a link suspension, they need to be "righter" than a leaf) but anytime stuff changes it can feel unsettling. As the springs on the outside of the corner flatten, both axles steer to the outside of the corner, likely at different rates so you can get some weird wiggles going. Hence a swaybar, you get less change in suspension placement compared to the frame and body so less of that suspension geometry change making things move around in addition to just feeling better because the truck stays flatter.
Crossover steering is generally really good about roll steer which is where the steering linkage induces steering wheel movement in articulation or body roll. This is why we do crossover, it's really good at keeping things consistent in body roll and OK in pure bump. But I think there can be some roll steer effects if the suspension's roll center changes and doesn't match the steering. And again a really good way to fix it is to just limit body roll with a swaybar.
All this geek speak means there can be a lot of problems you didn't know you had that are solved with a swaybar. And in most leaf trucks, you can't really change the causes of the problems to try to make the root cause any better anyway.
And to talk about bumps and dips in corners, we ran into some CRAZY paved road bumps and dips on the drive through Canada to Alaska for the UA trip last summer. Their frost heave is no joke. There was one that made me really glad we have a fairly predictable truck with 2.5" shocks on it and that I apparently have more work to be done on this side of the grave. I saw the whoops coming in a blind corner so I couldn't use more road than just my lane so I steered where I wanted to go, held the wheel steady and counted on the truck to keep the rodeo going where it was supposed to. Turns out it worked but I checked up a little after that one!