For me, bettering the breed doesn't really have to do with CHANGING the breed. I think the opening post was taking it a bit literally. Maybe instead of saying "bettering the breed" we should say "keep the breed alive" for me, you want to breed your foals to be good representations of the breed.
Take for example thoroughbreds. They are not being bred to stay sound right now. They are getting bred to go faster but not to hold up under the conditions they run in. Sure, there are tons of other variables, but for the sake of this conversations, that is the one I would like to focus on. Instead of breeding for this, I would rather sacrifice a bit of speed to start breeding for long term sound horses.
When you cross a stallion and mare that do not compliment each other, you run a larger risk of having a poorly put together foal. So to avoid this, I would say you are "bettering" the breed if you try and get a well put together horse. This way, regardless of if you jump, pleasure ride, cut cows, whatever, it will remain sound.
Obviously, you are not going to want the same thing in an arabian than in a quarter horse...but you can still try and better even your discipline by breeding for well put together foals.
I kind of rambled..but hopefully that makes sense.