Ideally, when you breed, you should be looking at the faults and strengths of both the mare and stallion to try to get a balanced foal (hah, come to think of it, perhaps we should approach marriage this way
) But seriously, if you know you want, say, a dressage horse, you're not going to want to breed two downhill, choppy-moving horses, in hopes of getting an uphill, free flowing foal.
Same goes with breeds. By definition, certain sports have requirements, and breeds have evolved to fit those requirements. Just like you see warmbloods in dressage, you rarely see warmbloods in western events because they just aren't built for it-they tend not to have as flat movement (which makes hours in the saddle a lot easier), they tend to not be as downhill (which makes it easier for QHs to keep pace with cows) and some would argue that they just also don't have the minds (although whether or not thats training is a different question)
Now, when you get into breeding crosses, a GOOD breeder will have a point, not "ohh, I love the spots on that appaloosa! let's breed it to that draft over there! Oh! he'll be the next jumping star cause he's pretty!" Instead, what a person needs to do is evaluate what exactly they are hoping the resulting cross will be. If you have an outstanding thoroughbred mare that is just lovely in movement, and mind, but you want her body to be a bit more thicker, and her loin connection stronger, and you wanted an eventer, you'd be smart to maybe pick a nice draft stallion, or a thicker typed warmblood.
Breeding is a crapshoot, no matter how you look at it. Some truly outstanding crosses have been made by knowledgeable breeders who took a gamble and it payed off. But often times, it hasn't worked out at all, and one only has to look at the overpopulated slaughters and rescues to realize that that majority of horses should not be bred