Ah, that totally makes sense!
Each horse comes with a different set of natural abilities. Gymnastics involves building on what he does well naturally but also encouraging him to move in the way he doesn’t, naturally. And then this changes over the course of training. Say a horse naturally inverts and falls on the forehand. You put a lot of work into getting him to stretch to the bit and lift the back and withers and step under behind. And then at a certain point you need to progress to collecting, raising the head a bit.
It’s true you wont get really good show piece lateral work before you have some collection, but it’s also true that lateral work is the foundation for collection.
My pet peeve (one of them, I have many) is folks who dont school any lateral at walk and just starting muscling the horse into trot shoulder in when they are “schooling second level” and it’s on the test.
And yes, Iberians come with some things factory installed that your average WB or TB may never really nail!