Too many team players result in too many meetings that decide nothing and make no progress.

yep, and to prevent that you need good team leaders.
in several companies i encouraged a regular developer meeting once a week. what i had in mind was a short meeting where everybody said in two or three sentences what they're working on, and if they have something important which concerns all developers, or most of them.
unfortunately it often happened that the meetings lasted way too long because several developers were giving lengthy descriptions of the problems they had what would have better been talked about in a team meeting with only the people directly concerned. the others were bored, so nobody really looked forward to the meetings any more.
i'm not a fan of hierarchies where hierarchy means power. but hierarchies where the people with the best communication and organizing skills moderate meetings and delegate work are invaluable.
there are companies which try to attract applicants by saying that the hierarchy is low (flat?). but the more employees you have the more you need a bit of hierarchy. only that the bosses should not be seen as the ones who make decisions but try to hear the arguments of their team and lead the decision process.

update: so i'd also say do not weight team skills too high but also search for people who can be team leaders. if they are good they can lead also loners into a good team.