In Ender's Game do you think Ender should become battle commander?
I think it is obvious from the very beginning of the story that Ender is the one who has been chosen as the ultimate commander. Rather than asking "should he do this," a better question is, "Is he the right choice?"
Clearly, yes, he should be a commander. From his very first moments in the game room as a Launchie, we see Ender standing back and observing the games of the older boys, calculating (accurately) ways to beat them. Then, he even figures out a way to socially earn himself the opportunity to compete.
From day one, Ender is different from the others. He stands out in intelligence, in problem-solving ability, and even in maturity. Certainly he should become a battle commander. And he does.