One of my trumpet teachers loves the Heimat tone. He used that to justify Renold Schilke starting on High C, and him doing the same. I like middle E personally, then working my way down with the Stamp workouts. I "cool down" on the lower ones, just to make sure I don't have any "funk" so I don't get odd muscles forming. I do agree with Rowuk that they are not rejuvenating or any thing such as that but sometimes it is relaxing to knock out a couple of low G's, like he said, as to relax our mind.
But I can say that for me, not warming down and making sure I ended with the right muscle memory caused me to shift over to the right side of my mouth, over playing is also another cause. But don't do something just because you saw it on TM, do what works for you.