It seems like good logic. What's your opinion?

Logically it does seem sound. I do a form of it without my instrument.

We musicians warm up to get the blood flowing and get the lips flexible. Then we play whatever we play. When you are done playing it is believed there lactic acid there. There is no lactic acid but there is lots of Lactate.

John's rambling - Here what is happening ::
Our muscles produce lactate. As we buzz our muscles go into an aerobic function. Lactate is fermented during aerobic exercise. This generates more lactate than can be removed and reslts in excess lactate. Normal muscle lactate levels at 1-2ml. When we play that lactate level jumps up to 20ml or more! I will avoid talking about transporters, isoforms, and oxidative capacity of tissues.But this extra lactate allows us to have energy production maintained.

What also happens is separate reaction where hydrogen ions are released which decreases the pH level of your muscle tissue. If you don't get the extra hydrogen and lactate out of your muscles and re-balance your pH level then you will have stiff and sore muscles.

To remove the lactate and hydrogen you produced you need to oxygenate the muscles. Runners do it by jogging lightly and slower and by massage. Cyclists do it by riding easier and slowing ot a comon cadence and massage. And WATER !!! Drink water after you play, it will help carry more oxygen to your lips. (not beer, or wine, water).

The lactate is then used to fuel what is known as the citric acid cycle. Which is going to get processed by your liver (another reason to drink the water).

So you should do some type of warm-down. But understand it is not to cool down it is to get excess chemicals out of your lips and return them to a normal condition. Which is a balanced pH not neccessarily relaxed muscles (although the two are associated with each other). Playing a cool down and not drinking water won't help much.

Our cross-country coach is really into the science of running, so I heard quite a bit of that last fall. Do you think that playing lower and lower would be a good cool-down?

Yes.
Playing lower and lower will loosen your emboucher allowing more flow of liquid. But you have to drink water to help the cleansing.

The goal is to dilute the waste in your lip muscles. So water and flexing is good. Low notes could be similar to a light massage; which is good. But again - water afterwards also. You must do both.

That's what I do, I spend around 10 minutes after a practice just to loosen off. I never used to do it but I have noticed a difference since I started doing it, it seems to have improved my stamina. Maybe that's just me! Muscles are better looked after I guess.