Competition.
There was competition everywhere in the world.
There were inter-civilization competitions, but in an environment that was gradually becoming stable it was to be expected; internal competitions also occur in peaceful civilizations.
After all, resources were limited, and no matter how large the living space was, it would be filled to the brim sooner or later.
Moreover, Earth was never all that big, to begin with, but nearly 20 billion intelligent lifeforms from all over the universe were crowded into the space. Even if the Protoss were to build multiple "space dimensions," they would still be extremely crowded.
Therefore, after the basic crisis of survival was solved, most of the natives - human beings - were squeezed out. Under the leadership of the Protoss, the biggest conflict on Earth gradually shifted from the external arena to the internal.