Tom I totally agree with your point on mutilating dogs for a fashion statement. Who comes up with these ideas like cropped ears??
I can tell you know very little about racehorses.
They are born to fly and believe me, nobody forces a thoroughbred to run! They love it and live for their morning workouts. 'Slow' horses are not shot, but re-assigned to a different job that doesn't require as much speed. They are many jobs a horse can have, jumping being one.
Now as far as broken legs, it's the reason why I left racing.
These horses are incredibly valuable (monetarily) and loved (emotionally) by their handlers, but sometimes they just cannot be saved and are euthanized. (not shot) It's absolutely heartbreaking and not taken lightly by those making this difficult decision. If possible, horses are always saved.