All my texts make it a point that in a differential rate law, the sum of the exponents on the reactant concentrations add up to the overall reaction order. However, I have yet to see any use in this. So you have two reactants, each undergoing a first-order reaction, and the overall reaction is second-order. So what? We analyze reactions for being first-order, second-order, and zero-order (at my level anyway), but that hasn't to do with the overall reaction order—just the reaction order pertaining to each individual reactant.
So my question is simple: what is the point of the overall reaction order? Why is it important?