I would think it impossible to breed a top-notch all around dog that excels at any given task. Reason being, what is desired in one task might be unnecessary in another. For instance...pen dogs are bred to work tight and close...a trait not so much desired in woods dogs. Perhaps cow dogs are not bred specifically with so much hunting drive.
In a perfect world, I too would like to breed all around working dogs but I'm sure not going to start culling my hog dog pups because they won't tree.
I see your point YBM...perhaps some of the pups that don't make the cut due to lack of hunting drive could end up making nice cow dogs. The problem as I see it is that same dog gets in the wrong hands and someone starts trying to breed the hog dogs carrying your name.
Without a doubt I agree more than 100% with your point about falling into the wrong hands. Guess I should have explained my own perspective. I like to see very few get to try their luck on cows off my dogs. If they do work exceptionally for that purpose they go to family members or close friends that work cattle and have the understanding that if they don't turn out for them they are no longer working dogs. CULL or I will do it for them.
The other issue I believe the closest thing I can relate to is what I call a meat dog. One that basically does it all. Bays cows, hogs, trees and runs everthing in the woods. I had one long time back. Great dog on everything I used her for but the saying "Jacks of all trades and Masters of none" I believe fits best.