I believe that you have a bias about "ideal teams".
The OP described the 2 profiles that you can find:
Side A: collaborative type
Side B: competitive type
When you work in a collaborative team, everybody unconsciously reduces their effort to a comfortable rhythm for the team.
When you work in a competitive team, everybody do their best, so they work at their own rhythm.
I experienced these 2 extreme environments, and the competitive spirit is the most efficient, BUT the collaborative spirit is more focused on relationships.
I believe a good balance is achievable, but you cannot reject the competitive profiles just because they don't fit your view of an "ideal team".
I'm working right now in a collaborative company, where people spend a lot of time about handshaking and various relationships activities.
But I'm very dissatisfied technically, since outside of relationships, the job is boring.
Before that, I worked at various companies which promoted technical excellence. It was much more interesting technically.