As I said: could you please describe an environment where competitiveness would _not_ occur?
^^^ CB: I'll have a go , in the spirit of cooperating with you, not competing with Miles :>)
How about an environment where there is no scarcity , i.e. nothing to compete over ?
In terms of a real, historical society of the future ( not an abstract "environment"), there might persist games of competition in "museums" which preserved our collective memory of the societies of the past, but these would not be competition over really important needs and wants. Sort of like who gets the most runs in a baseball game is not a really important, just kind of entertaining.
By the way, it wouldn't be an end to all struggle. There would still be challenges from the non-human environment to be met, such as the depletion of all oil reserves or the like (Of course, this has the danger of turning into scarcity and the return of real competition).
It would be a virtual end of dog-eat-dog competition between humans. Such competition would be rendered extremely rare, an anomoly.