Two additional matters occured to me as I read your post.
I agree we are taught to see and take advantage of divisions. This raises the old question of nurture and nature. To put it bluntly, I'm afraid that were we not taught division we would invent it anew on our own. This applies both to the external (political, tribal, territorial, etc.) world and to our own hearts. From my perspective, environment reinforces our inborn tendency toward division and fragmentation. We are born into the kind of world our species has created, and we have the created this world out of the inherent turmoil of the human heart. To put it another way, we have made the world in our own image: a divided heart.
As to the second matter, I quite agree with your point. We use our divisions in order to justify our drive to control. The ant queen's song in The Once and Future King comes to mind, the tune by which she incites her subjects to go to war with another ant colony. In essence, the song celebrates the supposed differences between the two colonies, which boil down to "they do not smell like us."
I also think, though, that a divided heart can lead one to withdraw from others and their struggles, to become only an observer. Frankly, I've not thought this through well. In fact, the possibility only ocurred to me as I read your post. Both of us know of legitimate motivations for such a withdrawal. Some, for example, do so out of a sense of vocation to engage in focused worship and prayer, which includes prayer for the creation and humanity. Others, though, learn just enough to see the dangers of the divided heart. They seek to protect themselves from others (and, perhaps, others from themselves) by retreat. This kind of pseudo purity of heart might serve for some as a first step toward what Jesus had in mind, but it must not become a destination.
Well, as I said, I've not thought the matter through--so I look forward to seeing what your fertile mind might do with it!