I was surprised to learn that toothpaste has a negligible direct effect. The overwhelming benefit comes from the brush action.
It's the secondary effects of toothpaste that provide its benefit. People tend to brush longer, more frequently and more regularly when using toothpaste. You are forming a habit, driven by the "clean" taste. Toothpastes usually have a mint flavor so that you "feel it working".
A light does of fluoride is the other benefit, but you can get the fluoride in other ways if needed.
I admit that I'm thoroughly conditioned to need toothpaste when brushing.