"Character driven" stories seem to have a lot more potentiality for darkness than action-driven stories, though. You build a well-rounded character by foregrounding the experiences that have formed that character, which invites more introspection; and unless you are one of those rare constitutionally cheerful people, introspection involves a lot of regret, nostalgia, mourning of losses, unhappy replay of situations you'd give your left arm to be able to fix, and the understanding that most mistakes just can't be unmade. If it's all carousels and birthday parties and kissy walks in the moonlight, your character is a joke, because no real life is like that: swings and roundabouts, rain must fall, etc.

With an action story that foregrounds plot, things usually move too fast for characters to have feelings or memories of any realistic-seeming complexity (and that's how fans of chase-and-kill-'em movies and shows like it, so there's a huge market for that). So yes, I think concentration on revealing character does by its nature deepen the tone toward melancholy. The most prevalent thread in the experience of mortal humans is loss on the way toward death, even if the losses occur through growth-spurts that take a character to higher levels. All of us experience this, and all of us think about it to one degree or another. Characters pulling a payroll robbery, not so much -- no time, too busy planning, watching for the cops, making your getaway. Characters grappling with ethical dilemmas that take time to resolve are more interesting (if that's your taste, as it is mine), but their doubts and questions do slow down and darken a story toward the tones of reality, even -- or especially -- in fantastic fiction.