Plunging cuts, and 'cove' cuts. Also smaller blades like dado stacks.
With a cove cut you move the fence to about a 30 degree angle to the blade, to get an elliptical cove along the length of a board. It's a rare thing to need. But if you really need a wide cove, it might be hard to get a router bit to do that.
Very beginner woodworker here, but dados(or any kind of groove are the ones that immediately come to mind. Essentially anything that has the work piece going over the blade, but not cutting through completely.
You can keep the riving knife for those cuts, it causes no issue. just can't use the blade guard. I honestly can't imagine a cut that would require the riving knife off.
Dado stack. It's a smaller diameter than the blade. You'd have to be pretty lazy to not just reinstall the riving knife when you put a normal blade back on, but I could see that happening.
I think people get complacent and if it a cut that one does fairly regularly, I could see someone saying on the 1000th cut "eh lets keep it off for this one time" and then it just becomes a thing.
With a cove cut you move the fence to about a 30 degree angle to the blade, to get an elliptical cove along the length of a board. It's a rare thing to need. But if you really need a wide cove, it might be hard to get a router bit to do that.