You’ll get a lot of argument on that from historians of the cavalry and war, as well as historians of the equestrian arts. For references, I’m not referring to some popular schlock book in which the same untruths are copied over and over from earlier sources making the same assumptions. here is such a thing as ‘traditionally incorrect history’.
Actually, I think modern dressage is a blend of traditional more extended movements together with many traditional highly collected movements. I think all of it developed in the riding school, borrowing and amalgamating elements from here and there, the capers and jumps performed in galas and carousels of hundreds of years ago, the courtly riding of an elite that regarded studying the equestrian arts as good for the education of the elite, right along with fencing and studying Machiavelli, etc.
For example, I don’t for one moment believe that the extended trot a top dressage horse does - is or ever was - an efficient way to cover long distances, nor that it has any resemblance in technical points to a road trot, strong trot, hunter trot, fence line trot, etc. It is different - because it’s a longer stride doesn’t mean it is the same, or developed in a direct line from something else.
Riding a highly collected horse in the battle field, having him wheel and kick at the enemy, having him leap in the air to clear a path - lovely, romantic thoughts. The study of the history of horsemanship and war and cavalry would clear that right up.