I think it is very much to do with how they are bred - as I said before. The young horse class horses, tend to be bred with enormous, flashy paces in mind with a back that doesn't swing. The horses bred to be superstars in the higher levels, are bred for good paces yes, but we also want swing and adjustability within the paces - not just going hell for leather in a big flashy trot constantly.
Also, the nature of dressage training. It is something that is developed over many, many years. A dressage horse or indeed a warmblood, is not considered mature until at least 6-7 years of age. We want to work them gymnastically, developing each step of the training scale. Perfecting each step before progressing. It is very much a sport for the perfectionist. To develop enough strength and balance for a horse to perform a movement such as the piaffe, or passage - and perform it true to its description - lowered croup, hocks closer to the ground, low stepping hind legs, high stepping fore legs, remaining on the spot or very slight forward movement etc etc etc takes years upon years of careful and correct training.
I believe the warmbloods are also less 'hardy' than your quarter horses - they seem to break down much more easily! As much as I hate to admit it, but warmbloods are not bred with hardiness and soundness in mind. Hence, we take things very, very, very cautiously to keep a horse sound at a high level into its teenage years.