But somehow, none of them ever became a cat or a cow.
Not over such a limited time span.
We are talking 100,000,000 - 2,000,0000,000+ years worth of time.
A lot can happen in a 1,000,000 years.
Just as Natural selection would predict. Only those completely ignorant of Biology and Evolution would think that a dog could be or should be turned into a cat or a cow over a few thousand years.
Humans used selective pressure to make them into the kinds of dogs we needed, hundreds of different kinds for hundreds of different purposes; we already domesticated cats and cows.