They need a certain mindset, which may be more common in certain breeds or family lines within breeds.
It is like developing any equine for doing certain lines of work. You start with animals who are successful doing this job. You breed them, then try to make them better at the job, bring in other successful working animals, to widen your base of blood.
Along with this is the huge EXPECTATION of the equine handler. They EXPECT to finish with the driving animal or whatever job they are breeding for. The handlers plan, do the homework, training and succeed, in getting the animals of this breeding to do their job well.
Some breeds are renowned for being multi-purpose in skills. Morgans and Saddlebreds immediately come to mind. The young animals of these breeders, are usually driven and ridden. Many European equines were both ridden and driven, with Lippizans, German breeds probably the best known in the USA. In the past, pretty much ALL the young horses were expected to both ride and drive, including Arabs, TBs, Hackneys, because they were more useful to their owners.
The more focused breeding, developing specialists within breeds, is a more recent development in the last 30 years. All-Around champions in breeds are not as common or skilled, as they used to be. Body styles are too different now, even within breeds.
Not really any different than breeding cattle horses. Some lines have cow, speed, were more heavily promoted with these qualities. No use trying to cut cattle on a horse who dislikes cattle! Roping off tiny horses who are not big enough to stop a cow is silly. You breed animals who are successful at the job.
We have Cleveland Bay crosses. Cleveland Bays have been bred for over 200 years to a standard body style, inspected to ensure quality before registering. There is greater similarity, from using closely bred horses in the last years, has a small gene pool. They are very similarly made, often related. They have been expected to be an all-purpose breed, suitable in build for many jobs, ridden and driven, sound in work.
They have a good mindset, but need a light hand to manage them. Not suitable for beginners in most cases, very smart, learn quickly, good or bad. However they are very accepting to skilled handling, willing, cooperative without being over-reactive. Great minds, but they need the good, consistant handling to bring that out. Otherwise they can be quite “opinionated”. Having many driving animals within the breed over the years, chances are high, that a Cleveland Bay horse WILL drive.
Some won’t, but that can happen in any breed known for a special skill. Some animals in that breed just don’t have the mindset to do the activity. You call that “Atypical” because he does not fit the average of the breed.
I do think that Driving horses have to be very cooperative, accepting of situations, willing to work with people, takes a great mind to begin with. Many nice animals are chosen, but not all are successful in finishing as Driving horses.