It would be interesting to see if the problem is greater with show cockers or working bred working cockers. I know from the conversations I've had with Nicola about Hearing dogs that it appears more prevalent with the show cockers at Hearing dogs but this could be different here.
I think along with being a gundog, cockers are a feisty, intelligent and in the case of food, greedy, breed. Historically biddability in working cockers was the prime trait to breed for in the breed but this is changing with preferences for size/colour etc with the massive pet breeding going on and this could also be a factor in their behaviour.
Lovely, the principles of training your labs are the same if you want your cocker to work. I also think if you have a pup in the house that you are going to be training to work you deal with it slightly differently then with purely a pet and as you've said previously, you don't chase them if they have something they shouldn't, you don't play tug games, you don't allow them to chase game/people/bikes etc, they're not allowed miles away from you off lead, you praise them to the hilt when they have something in their mouths and they bring it to you - and even more so when they willingly give it to you. You're always thinking of what your adult dog should be doing in the field so the behaviour you want as an adult dog is instilled very gently very early. This doesn't mean the puppy is deprived, far from it
Perhaps we should be paying more attention to the gundog element of their being even if they're not working dogs?