There is no such thing as unselfish cooperation because people always cooperate for their own selfish reasons. Even a mother who tends to her children does so for innate selfish reasons which is to propagate her genes.
You can have plenty of productive cooperation without a need for competition, but there has to be something in it for the people who are doing the cooperating that motivates them to utilize cooperation as the prefered strategy.
For example, 10 hungry people may fight over a rabbit, but are likely to cooperate to kill an elephant.
The act of competeing by itself does not gaurantee good results unless the people who are competeing against each other are doing it because competition is the prefered strategy. If teams are competeting against each other, then you have a cooperative-competitive system. If secrecy between teams is not an issue, then the competing teams can share their results with other teams, which improve overall performance.
In essence, a group of people will perform poorly unless there's something coveted to be gained by doing it with excellence. Peopel won;t work well together unless there's a shelfish reason to work together.
Making more money does not motivate people very well.
If money really did motivate people, then to improve performance, all you would have to do is throw more money at the situation, but that usually never works, and may even make people perform worse (eg Wow, now that I have more money, I can get away with doing even less - if they throw more money at me and I'll be able to quit and go on a long vacation).
I think that in a natural setting devoid of artificially induced motivation, people will always tend to do only what is needed to get by reasonably well and no more.
As I said, we can talk about this for hours and never agree on what works best.
Your point about Ed Deak has been noted, and I am very much interested to learn what his ideas are.