What breed would that be with such a huge gene pool, and I assume no other health issues?

There are other health issues & tests for most of them, however for a dog/bitch with a very uneven hip score, the dog/bitch would have to be unique in some way as there are many fully health tested dogs within the breed with even good scores with the required work related/character traits available of both sexes that would be have to be bettered in some way for them to be disregarded for the dog/bitch with the poor score.

The problem with breeding for "acceptable" scores/temperament/tractability/character etc is that it leads to dogs that are acceptable rather than better than the previous genertion

>According to population geneticists no breed has a wide enough gene pool to exclude the majority of animals from breeding which aiming for 'perfect' anything will do.

Lots of people mistakenly equate a large population with a large gene pool.