Andalusians and Lusitanos when breed and broke correctly are the what the dressage horse is. They were the original ones that were used in baroque dressage. There are some lines out there there that move “like sewing machines on speed” like one of the first posters said but that is not the majority.
The reason that they are not more popular in dressage (at least here in U.S. and most European countries (and forgive me if I’m repeating here I didn’t read the whole thread)) is that they are rare and until recently they were very hard to find in the U.S. also in a lot of Europe they have their own breeds that they use.
As far as what an Andalusians temperment is I haven’t worked with a more beautiful minded horse (I have handled most breeds in my line of work). They have an amazing work ethic are for the most part smooth and easy to ride (there are some lines and horse out there that are not just like every breed) they have natural push from behind and natural extension through the shoulder which makes it easy for them to preform to the high levels of competition.
They are smaller then your typical WB (obviously) which is another reason I believe that they are not more popular. in face of the WB revolution they don’t quit measure up.
Also consider that Andalusians, Lusitanos, and Lipazzans all come from the same lines and are generally the same breed. They are from different parts of the Iberian peninsula but you will find that they are all PRE horses.
With this in mind the highest level of dressage riding is the Spanish Riding School and what do they use and train as their mounts?
If you’re interested in some lines and breeders feel free to contact me!