I remember a hygienist at the dentist once telling me that toothpaste isn't a huge deal and that it's the mechanical friction of the toothbrush that provides most of the value. Since being told that, after a meal, I often wet my toothbrush with water and brush for 10 seconds or so.

I just researched it some more and from what I understand, after eating, food debris that remains on your teeth forms a sort of biofilm. Once the biofilm is formed you need those traditional 2 minute long tooth brushing sessions to break it down and remove it. But it takes 30+ minutes to form the biofilm. Before it is formed you don't need long brushing sessions to significantly reduce the amount of debris that is left on your teeth. So then, these short informal brushing sessions after meals seem like a great "bang for your buck" in terms of reward vs effort.