1) Why does "serious" have to equal "grimdark?" Why can't a portrayal of a benign, functional society and lessons on how to live cooperatively with others in such a society ("Friendship" as the "magic" that "makes it all complete") qualify as "serious?"
2) There is already plenty of "seriousness" of the dark-ish sort in the show, it's just crafted so that its presence is open to interpretation.
Twilight appears to have been so traumatized by her experiences in Magic Kindergarten that the possibility of being late with a single assignment. The prospect of being sent back there, no matter how remote, was enough to make her come unhinged and start using mind-control spells on children. We can join the target audience in just enjoying the show as comedic cartoon fun. Or, if we want to be "serious," we can start to wonder: just what do they teach in "Magic Kindergarten," and how do they teach it, if the experience is enough to leave a young mare scarred for life? Alternatively, if Twilight is just extremely oversensitive and mentally fragile, is it wise to trust her with huge amounts of magical and political power? Why is there no regulation of dangerous magic and no societal effort to keep it out of the horns of mentally unstable (Twilight) or criminal (Trixie in Magic Duel) individuals?
Twilight isn't the only one deeply wounded by her childhood. In Cutie Mark Chronicles, we see that both Fluttershy and Rainbow Dash were bullied as fillies, apparently with no adult supervision to keep it in check. The taunting drove RD to become so competitive that she doesn't even notice that the friend she entered the race to stick up for is plunging to her death. If not for the "lucky" appearance of a flock of butterflies, and their wildly improbable ability to catch Fluttershy, RD's "victory" in the race could have had a very tragic outcome. For her part, Fluttershy is quick to abandon her home and family as soon as she meets some friendly animals. She's a young child when this happens, and no one tries to stop her or at least see to it that she has somebody to look after her. What does this tell us about her prior life in Cloudsdale? The explosions of pent-up rage that get out every once in awhile (especially in the Iron Will episode) are another indication that all is not well in the city of clouds and rainbows. In the same episode, we're given a glimpse of a sad and miserable filly Pinkie (Pinkamena Diane) Pie, whose childhood left her with symptoms bordering on Multiple Personality Disorder.
Race and Class:
The culture of Equestria is aggressively pony-centric, even though there are numerous types of non-pony sapients in its world. The place names, the language ("anypony," "nopony," etc.) the political structure (only ponies have political power) all point to a world where ponies are a highly privileged race. We (English-speaking--not so sure about other languages, e.g. Chinese) humans, who do not share a world with other sapients like us (no elves, dwarves, orcs, griffins, dragons, etc.), employ a much more inclusive and species-neutral set of linguistic conventions. As an audience, we could just Enjoy The Show and take all the pony-isms as a fun layer of flavor for a show about little candy-colored ponies... Or, if we want "seriousness," we could view Equestria as a brutal pony tyranny, with most of the unpleasantness kept out of sight. Consider: the Apple Family's livestock are people...of other races. There's a term for that, I think it starts with an 's.'
If we imagine aliens watching a show about life in the Palace of Versailles, but without seeing the exploitation and squalor that made it possible, perhaps they might think that Earth was a lovely fantastical utopia, start calling themselves Humies and fantasize about coming here to leave their own mundane, imperfect world behind. Sun King...Sun Princess... Hmmm.
And so on. The "seriousness" is there, if you want it. It's just subtly-placed enough that the viewer can choose to see it, or not, as a matter of interpretation. Which is brilliant, IMO.
Moving beyond the "dark" aspects, there's plenty of other levels of seriousness in the show, such as the esoteric and scientific symbolism hidden in plain sight, or the chain of synchronicity linking the M6 together (Cutie Mark Chronicles) long before they ever met, implying a subtle form of transcendent guidance and intervention (in Fluttershy's case, acting to rescue her from a premature death by breaking physics with a flock of butterflies) in their lives. There's metaphysics and myth and mystery aplenty. The show is already very deep. It doesn't need grit, zombies, more violence, or more evil to make it a serious show.
One more thing:
Question: Why can't FiM be more like [insert other cartoon here] with its scarier villains and more serious themes?
Answer: Because it's doing a very good job of being like My Little Pony: Friendship is Magic, and it ought to stay that way.