It's more about piece of mind for me. I've used one without a splitter for years without issue, but it's always in my mind that if something happens and the offcut piece get's twisted and touches the back of the blade, things could go wrong pretty quickly.
There is "gets twisted" and there is "twists".... a big difference.
When cutting some woods the kerf may tend to close up and pinch the blade, either stalling the saw or propelling the work over top of the blade back at the operator, however, I have not had that happen to me.
I have the blade stall and then I simply shut it off with no harm. In either case, there is no "twist" involved.
As far as the offcut "getting twisted" ... that can only be operator error, if it's possible at all. Your feed pressure should never be on the offcut, only the piece against the fence.I have great difficulty seeing how the condition you describe would happen, but I could be wrong.
The piece against the fence must be controlled, not just push/shoved through. Controlled means held down, pushed laterally or to the right against the fence, and finally pushed forward. Your thumb position is important for this lateral control and can "steer" the work when pushed forward. At some point in the cut you will lose the ability to fully control the piece and that's when you reach for your push block. A good push block will allow you to feed the work, forward, press it against the fence and hold it down on the table, all at the same time. There are NOT many push blocks that are good at all 3 aspects.
The riving knife or the splitter helps maintain the lateral pressure against the fence, however slight. At the minimum, it will not allow it to rotate away from the fence. This is the "other" function which I described above, as is not well advertised and in some cases, and not even mentioned.
Plywood and other sheet goods are not known to pinch the blade at the rear because they are stable, unlike natural wood which may have tension grain internally.
Plywood WILL come away from the fence if there is no splitter OR the operator does not maintain proper control. Don't ask me how how I know this. :frown2:
You can operate a table saw for years without fully understanding the physics involved and have no mishaps. It's much better to understand the physics of any machine with rotating cutter or blades to be a safe operator. :smile3: