But that's the problem, the general populace doesn't seem to even be rooting for the Order or know much about them at all. They're a minority of rebels in a society that doesn't notice that demons are this close to ripping the world apart. They've been fed crap about Dante being a terrorist and maybe they believe it, because most of them are going about their lives just fine and Dante appears to be introducing trouble. So let's say the Order does save everybody - who's going to care if they didn't know there was problem to begin with? Heck, they may want to throw the whole lot of them in jail for treason, if they think the legitimate government is good. Vergil's not going to get power and glory by doing just what he's doing. Perhaps he really does only want to save the world and doesn't want power at all, but then, what kind of foil would he be to Dante? Where would his conflict lie? Perhaps DmC will introduce something brand new.
Maybe by the end of the game, everybody will see demonkind for what it really is and cheer for any force fighting against it. Or maybe Dante and his allies will be unsung heroes and go back to being largely ignored despite saving the planet, like the end of every other DMC game. It depends on what direction the game chooses to go, but there's a reason why the classic Sparda locked away his power to let both worlds rule themselves in the end.