Should Martin Luther have tried to keep the Church from splitting up? Why or why not?

This is a significant question, because the effects of the Protestant Reformation are significant, and have created ripples which have continued into the present. At the same time, be aware that the Reformation itself was deeply destabilizing, and resulted in a great deal of sectarian violence and religious warfare. In any case, this answer is really an opinion question, so I can't address it as a yes/no answer. That being said, I do have a few thoughts of my own, as they apply to this question.
First, be aware: Martin Luther's initial intention was not actually to divide the Church. Rather, his intention was to reform it. He genuinely believed that over time, incorrect doctrine had made its way into the Church, and he was trying to return it to (what he believed was) a theologically correct understanding. Furthermore, if we consider the stakes, especially in a period which was much more intensely religious than the western world is today, keeping silent would have been anathema from his perspective. One can disagree with his theology, but there's no reason to suggest he was insincere in his beliefs. With that in mind, is it realistic of us to expect him to recant these ideas, especially when they related to some of the central tenets of the Christianity and (perhaps most importantly) would have potentially impacted salvation?
In any case, I'd also suggest that these divisions within Christendom are better understood more in the manner of ripple effects, rather than anything resembling his initial intentions. With that in mind, after a certain point it is also worth asking just what kind of steps he could have taken to prevent the Church from breaking apart, and whether these suggestions are actually realistic. Keep in mind, there were Protestant theologians and preachers far more radical than Luther himself, and that, even were Luther to recant, we cannot expect they would have done the same. At a certain point, a movement outgrows than it's originator, and I believe this was the case with Luther. Even were Luther himself were to reverse course, to what degree would we expect other Protestant preachers, to say nothing of the various the princes and polities in whose lands Protestantism had become entrenched, would reverse course also? Your question asks whether he should have kept the Church together. I'd respond by asking if, after a certain point, such a goal would have been possible at all.