I haven't encountered yet that I couldn't achieve something with my cavesson.
I ride transitions forward and back, make bends, stops and I even achieved making a stop with my panicking horse without a bit. That is the reason why I train the one-rein-stop often, so it becomes a reflex.
I also ride lateral movements with my horse (my seat is more important than the reins, because the reins just tell the horse how much his head is turning.)
For calming my horse down I don't need a bit, I have another very good exercise for that.
So, I do not need a bit right now. But my horse is also not done with changing all her teeth/molars. My horse is not that far in her education, so may be we will need a bit in the future. But may be we will never need one. We will see...
I think it is hard to make a generalization about bits: that all/none horses need one. May be it it also dependable at the discipline and/or level that a combination is.