I believe that most runners warm up in the first few miles of a long run by starting slowly. A cool down can be achieved by jogging the last mile, although many runners like to finish moderately fast.
If you're asking whether separate warm ups and cool downs are the most effective way to increase mileage on long run days, the answer is no, it would be better to increase mileage with doubles or longer uninterrupted runs.
If you're looking a reason to tell your coach that your friends on the internet disagree with him, forget it. A mile warm up and cool down won't hurt you, and he might be doing it to make sure you're regrouping as a team or to make sure you're stretching before and after.