First off, this was really well thought out. It is important to get such a definition from a Liquidity provider as yourself because I think you are in a better position to explain what many people, economists included, struggle to grasp as an entirely new way of transactional relationships.
I bet the reason why there is a widespread consensus of the definition (that you disagree with) is because people were too lazy to ask and answer further questions in other to understand how the liquidity pools work.