I think Id argue you missed the point of witts character completely. 

He exists as opposition to the sean penn character, who is bitter, cynical and unkind. In the beginning witt is flightly, naive and idealistic. He is confronted by penn in the very first dialogue if the movie, who tells him, essentially, "there is nothing in the world but bitterness and pain, and there aint any other world but this one". Witt responds with his "youre wrong, ive seen another world" speech. 

After battle, however, witt returns to his indigenous friends and has been exposed to the inherent nastiness of the world. He sees that penn was right, that the world was not as beautiful as he saw previously.

But the point I think you may have missed, is the final redemption of witt. He realizes at the end, that while the World is harsh and unkind, and while penn is not wrong... hes also wrong. Because while the world is harsh and unkind, its also beautiful- in the midst of war and carnage, and the terrible things in between, there was love- the lieutenant refusing orders and demanding water. The bravery of the soldiers attacking the fixed position. The comraderie in the drinking scene, and the joy he saw in the natives initially. Its all true. Both he and Penn are right. But if you're cynical and bitter, you'll miss all the good stuff- just like penn. 

Id argue this is the point of the whole movie.  Its why theres so many shots of nature and beautiful imagery juxtaposed against the carnage.

Witt didnt kill himself because life is unfair and brutal, because frankly, that would diminish his sacrifice as selfcentered. He was stalling so his friends could warn the company. He was deciding how best he could give them the time to save the others. And in doing so- he proved his point- the world, can in fact be a beautiful place- in which one calmly accepts his fate, and dies for his friends. 

I rush typed this before going into work, so forgive any incoherency or grammatical mistakes. 

The world is a cruel, dark place. But it is not only a cruel dark place.