What sort of cuts would cause you to need to remove the riving knife?
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.
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.