@Cyracuz,
It may be true that we overvalue the competitive today, but I think it would be wrong to seek to eliminate it. Empedocles seems to have expressed what I mean when he taught that the basis of reality is "love and strife" (Eros and Eris), meaning attraction and repulsion. (Even nowadays, that's pretty good physics, if nothing else.) One finds something similar in Taoism, of course.
What I think it means is that a reality consisting only of attraction, of goodwill, of agreement, would end up stagnant, dead. Like it or not, there has to be a countervailing force of opposition to keep things moving and circulating. I think you hit on that when you said "We have to reinvent and redefine our valuesystem" etc., which would involve trying new variations on what we embrace and what we reject.