Levels of competition within a given collection of organisms is relative - the cells of the human only occasionally compete directly - in the rebellion known as cancer (which clearly isn't the norm).

Not all societies compete at the same level but levels of competition also depend on the level of technologies and resources available. English society didn't stay in permanent civil war when muskets were introduced but you can see situations where the introduction of muskets and potatoes cause civil wars in societies where they were introduced [1].

Now, in the US since WWII and especially since the 1980s, an increase in resources has been channeled to allow society to become more competitive. One could easily imagine that if this trend continues indefinitely, things may well reach the level of something akin to civil war.

Edit: whether one see cooperation as a mean of competition or competition as means of cooperation is kind of a matter of taste. An army facing another army can experience toxic levels of internal competition that prevents it from being effective against an enemy (or oppositely, it might experience a lack of "killer instinct" before the key moments I suppose).

[1] https://en.wikipedia.org/wiki/Musket_Wars