People will understand a difference between the following, but they're worth clarifying. Conscientiousness does not imply a perfectionist personality trait. It means, for example, that work is done to a best ability, and not out of neurotic obsessive compulsiveness. It's just the right thing to do. That's an all-round positive.
Work can be carried out to the same equivalent level by a perfectionist, but their attitude is likely to impact on other people, perhaps in term of unwarranted criticism.
The Roman Catholic church lists some hundreds of saints which it asserts were perfect. Pope Francis might struggle to join them, because despite being the representative of Jesus Christ on Earth, and through the mystery of the Trinity, Christ, the Holy Spirit, and God the father, are equal, and furthermore, his papal infallibility, in recent times, he was irritated into hitting someone, as caught on camera (see video).
As a more numerate than literate person, I doubt perfectionism through mathematical sense and logic. But conscientiousness in all its aspects is very desirable, as it overlaps positively with moral, ethical, occupational, social, political, and even religious aspects. Like everything else in my thoughts or opus, it propounds a more internal rather than external basis. The personality trait 'perfectionism' on the other hand, can easily spread from one person to others, and that tends to happen if it's uncontrolled, whether its impact is wanted or not!