Phantom

Current quests are pretty pointless as to what's going on. You go somewhere, do something, get something, and that's the end of that.
To top it off, there's nothing that other classes can't do either. Everyone has the option of participating in everything.

Storywise, though, the Heroes, the Royal Army, and the People's Militia of Edelstein all have a story-based obligation to fight this war.

Heroes: People close to them have suffered. Mercedes intervened because the Black Wings were threatening the Elves (a gesture Mercedes, as Queen, took as a declaration of war against her people and her allies); Freed and Afrien wanted peace in the world, and their goals are a factor in their involvement; Aran did it because he's noble (and in the Second War, did so because he needed to finish the job he didn't the last time); Phantom's in it because the woman he loved died by the hands of the Black Wings.

Royal Army (AKA Cygnus Knights): As the only REAL official army of the Maple World, they have an obligation simply out of their status as rulers of the humans of Maple World. Cygnus cares about the kingdom she rules, so she obviously participates because of this.

People's Militia of Edelstein (AKA Resistance): They had their sovereignty taken from them, and their rights/freedoms dictated by a tyrant. Not to mention that Demon Slayer lost his mother and sibling from a backstabbing betrayal. For Demon Slayer, his is a quest of revenge, much like Phantom's (difference between them being that Phantom had noble origins, whilst Demon Slayer is a defector). However, for the Resistance kids, it's a rebellion, much like the American Revolutionary War (in a sense).

Explorers: Think of them as hired arms. Mercenaries, if you will. Their involvement is out of choice, and many choose to do so with a "Soldiers of Fortune" mentality - they fight because they are getting paid and seek wealth/treasure/fame. Others fight out of a sense of duty/moral obligation. Some will fight simply because they're bored. And then there are those who fight to defend the world they love, not unlike the other armed bodies involved.