We do a pretty hefty bit of exercise in my Shidokan class but I'm with you Moosey. I think it should go at the end where you can really go for it and leave all your energy in the dojo knowing that that's the last thing you're doing. I don't run the class though. The only real benefit I can can see is that you learn to execute techniques while fatigued and to keep going. A similar thing is used in BJJ classes.
In both the arts I've studied for any length of time we always did a load of Press Ups, Sits Ups and either Squats or Squat Thrusts. and as described before, in my current jujitsu class all the Brown Belts go through the 30 Throws, which is done at speed just to knacker people out (and to help drill it for the Shodan Grading) but the idea of the 30 throws is to knacker the student out at the start of the grading to see if they can still perform well when knackered. When I did TKD in my teens one of the Black Belts was training to join the Marines, and the instructor started getting this Black Belt to run the warm ups, and we were expected to keep up (or punished with extra squat thrusts -_-) and after a couple of weeks most of the class were keeping up with his 75 press ups a minute and 75 sit ups a minute >_< i remember when i used to be fit . . .
As already mentioned, it's mawashi uke. My personal opinion is Sosai thought it was a very important technique and did not want it to be neglected. So he incorporated it into our warm up exercises with twists and bends to not only work on the technique but also flexibility.
5 sun salutation a and 5 sun salutation b at 5 am gets me going for my morning bjj workout and my life.
I tend to warm up with... Some Capoeira ginga. Starting slow, gradually moving quicker, changing direction, twisting and rotating the torso. Shadow boxing. Starting with punching, then adding elbows, then knees, then (slow and low) kicks. Half speed mostly. Always moving, and using footwork. Sometimes I skip for a couple of rounds (or until I get tired of whacking my feet with the rope). Then joint rotations/mobility. Starting with the ankles/toes then moving sequencially up the body. I have certain movements I favour. Sun salutaion in parts for example (as mentioned above). Then I move onto the floor and do some rolling, BJJ flow drills and yoga postures. Then I usually stop training as that's quite enough of that "physical activity" stuff.
Here is some advice..might come handy to someone Best thing to do is divide warming up in two parts. First is general and second is specific. General would be easy running for 15~ minutes, warm up joints (neck, shoulders, elbows, wrists, knees, ankles), and easy and short stratching of major muscle groups. All together it should take about 20-25 minutes. Specific depends on what is going to be trained. For martial arts which includes lot of kicks (Taekwondo, Karate..) progressive and specific dynamic stretching works great. For arts including for example small joints manipulation (Hapkido, Ju Jutsu..), wrists and ankles should be warmed up more (joint flexion, exstension, circular motions..). For arts including leverages on body extremities and large muscles groups (Jiu Jitsu, Judo..) whole body should be properly stretched once more. And while you can miss stretching up if you have continuity in training, you should never start train without raising body temperature - warming up, which prepares your muscles and joints for hard work. If I am planning to do sparring I take full warming up as I mentioned here..If I am going to do only forms/tuls I only do general warming up and then progressively add speed and power to forms/tuls.
I teach one hour classes so I keep my warm up to within 5 minutes and the movements need to overlap with core skills and drills. We always start with joint mobility exercises then move on to either rolls, a hand eye and guard coordination game, or straight into slow drills. All drills are done slow through to fast in any case. Stretching is done mid class or end of class if it is done at all.