The prisoner’s dilemma is a mathematical example to introduce students to different models where cooperation and competition have different outcomes. You can also design game theory systems where competition is generally a prefered action. The actual question is which model better reflects our contemporary realities, but regardless, there are great arguments to claim that cooperation is better most of the time if we assume that the participating actors are aware, intelligent and capable of taking free decisions.
I mean, sure, that will solve some things. Not climate change, though. I think we can aim for a little higher, but when I say that perhaps seeking infinite growth in a finite planet might lead to an environmental catastrophe that’s somehow controversial.