Wow--three new posts all in the time it took me to write this one! I'm going to read through them and then edit as necessary.
I agree about the Guillem syndrome, Alexandra, but wasn't Balanchine promoting high extensions before she became famous? I remember a passage from "Choura," by Danilova in which she says something to the effect that her students at SAB are always stretching--"they tear their legs apart"--and that she would say, "How high can you do developpé? Higher than your head? Why don't you work on your two pirouettes which are not so hot instead?" I'm not sure when that book was written, though, so it might have been around the same time Guillem was becoming famous.
While I admire Sylvie Guillem in many ways, I'm not really a fan of hers. But somehow the high extensions look different on her. I don't know if it's the Paris Opera training, but it's as if extensions that high are entirely natural for her, and so she was able to work on other aspects of her technique while maintaining the high legs. Also, people tend to ignore the fact that Guillem also has that lovely Paris Opera port de bras, a voracious jump, &c. One thing I do notice about Paris Opera dancers (although this is only from video) is that while they do all seem to have those gumby-like bodies, they don't work exclusively on raising their legs.
And you're exactly right about the multiple pirouettes. If one has good balance and strong abdominal and back muscles, s/he can turn because the hip joints aren't really integral to the movement. Petit allegro does use the hips extensively, as dancers are taught to do beats "from the thighs" rather than merely beating the feet.
What appears to be happening at the Kirov (and by extension, probably at the Vaganova Academy) is that they choose dancers who are naturally very flexible. However, unlike at, say, Paris Opera, it looks as if the dancers are encouraged to stretch, developpé to the sky, &c. all the time rather than only working on it during adagio combinations.
I noticed this immediately when the corps women came out doing grands jetés in a circle during Act I. The Vaganova method teaches that in order to do a high jump, you first do a strong, quick grand battement with the front leg. This brings your hips and torso up into the air, and then the back leg comes up so that the action of the jump follows an arc in the air, as if the dancer were leaping over a hill. You probably will not see a split in the air.
With their super-flexible, weak hips, the dancers have the ability to throw the front leg up, but they don't raise the pelvis and torso into the air. Thus, the jump makes a straight line in the air, the front leg is often higher than 90º, and the back leg droops. The overall impression is one of heaviness and effort rather than lightness and ease.
In terms of petit allegro, this will probably sound weird, but the Balanchine style actually requires less
precision than the type of petit allegro Vaganova-trained dancers are used to doing. It is not essential that the heels stay down during pliés--which makes it easier to "cheat" and do certain movements, such as consecutive pas jetés, faster--a perfectly turned-out fifth position with the feet "glued" together toe to heel is not important, and fifth is allowed to be over-crossed. (That over-crossed fifth has done some strange things to NYCB's technique too--beats so crossed you can't see them--but that's another thread.
Anyway, a beaten step such as entrechat-six, jeté battu, or brisé requires extremely strong, minute control of the adductors (inner thigh muscles that pull the legs together). When the adductors are stretched out as much as they are in the current Kirov bodies, the dancer gives up some of this control, giving beats a weak, unfocused look instead of a sparkling, "snappy" quality.
The degree of care taken when the feet are on the floor during petit allegro is generally what determines speed. Once in the air, a dancer has a limited amount of time in which to beat the legs, so the time taken to complete a step, say pas jeté battu, doesn't vary much from company to company regardless of style. What does alter the time taken to complete a combination is often how picky one is when it comes to doing an obsessively perfect fifth position on the ground. If you look at a Vaganova-trained dancer from the side, s/he will probably have a fully-rotated, "glued together" fifth position with the heels firmly on the floor every single time. Most other dancers sacrifice a little turnout (it still appears turned-out from the front; I wouldn't really consider this a technical flaw because the turnout muscles are still engaged) and Balanchine-style dancers tend to keep their heels a little off the floor--that is, the second the metatarsal areas of their feet touch the ground, they're already pushing off into the next jump.
So historically, Kirov dancers have tended to have slower petit allegro not because they can't beat, but because they are so concerned with with making every position on the ground perfect. (I don't think they should be criticized for that.) The beats themselves were brilliant, and it is that brilliance that is lacking in today's Kirov dancers.