Why, specifically, do military historians have to justify their field? War is not a joke, but neither are most subjects historians study. The Holocaust, slavery, colonialism, and violence against women are all incredibly grim topics that have been studied a great deal of attention by historians as well as scholars in other fields. If we are restricted solely to topics that are pleasant and give us happy feelings to read about, I imagine we wouldn't have an enormous amount of material to work with. The human experience is vast, and war/organized violence are an important dimension of that experience. Certainly one can argue that military historians as a field sometimes tend to glorify war, or that a particular kind of military history receives an undue amount of public attention and popularity. But that to me is a criticism of the direction of the field, not a valid critique of the field itself. If bad examples of a field of study disqualified the field from being considered proper avenues of historical study, then the entire concept of colonial studies would have to disappear because of Niall Ferguson.

As for the argument of "more important," I find that pretty facile and ridiculous. It's funny you mention art history as an example of being "important," as art history is a frequent target of people making similar arguments. In fact, the entire field of history is often derided as a useless major that's not important or worthwhile because it doesn't make money. Historians study many things, from medicine to art to food to thought to history itself. I don't think we should look down on any potential avenue of research because someone doesn't think it's inherently "important." It wasn't so long ago that any history that wasn't primarily focused on high-level politics and military engagements was derided and considered less prestigious. Just because you personally don't find it interesting doesn't make it inherently less important.