Active cells make waste. While the supply of fresh nutrients comes to your muscles under pressure, the return route involves being "pumped" by the action of your muscles. If you stop cold, your muscles are still making waste products, but without any muscle contractions this stuff just accumulates. Stretching is a good way to keep it all moving. It may still be placebo, but there is a physiological reason for stretching to work.
The second problem involves the meal break. You only have so much blood, and if you put a meal into your belly, then your body will try to make use of it. That involves moving blood to the intestines to bring those goodies on board. It takes a while to stop this reroute and get the blood back into play for your muscles. If you have a big meal and then ride hard, this digestion interruptis will make itself known somewhere in the lower end of the digestive tract, and it won't be pretty.