Actually, the Maliki position you mentioned is a minority position, though it is the majority position of the Hanafis. The Maliki majority consensus is that, so long as the dog is alive, it is pure (najasa). This is because dogs are animals, and all animals are pure when they are alive

Upon death, unless they were killed in the name of God for a clear purpose and killed in a way that minimizes pain to the greatest feasible degree, they are impure to touch (this, of course, is the basis of “zabihah”). However, transforming the remains of the animal, for instance my tanning its hide, removes its impurities. Thus, Malikis will say that pig leather is pure, but boar-bristle brushes are impure, for instance

The other Sunni schools disagree with this, and I believe the Jafaris come to somewhat similar conclusions but using a different logic. I’m afraid I’m not quite sure, though