This entry has a severe shortage of negative reviews on both MAL and Anidb, so I'll contribute my opinion to keep people like me from wasting their time with these 24 episodes.
Scrapped Princess is about Pacifica, a princess who is prophesized by this world's religion to destroy the world when she turns 16. As such, she was abandoned as a baby by the king and found by a family who have been guarding her for her entire life.
As a thematically focused series, Scrapped Princess fails on every account, but that will take time and spoilers to explain so I'll comment on more its more basic aspects first. The plot meanders too much in Pacifica's episodic travels and has large exposition dumps that diffuse all of the mystery in its setting at once. The places where the plot meanders is also used to introduce characters that react to Pacifica's status as the scrapped princess. However nearly all the characters have bland personalities and backstories that aren't worked on enough for you to care for them. They also all turn out the same way; they see Pacifica and decide that such a nice girl can't possibly destroy the world so they defy religious prophecy and the government. From what I can tell it seems like their further desire to risk their lives to protect her is mainly motivated by their observance of Pacifica's character but the problem is that Pacifica herself doesn't have the charisma or magnetism to pull that off. The other thing that the plot tries to do is constantly remind you of Pacifica's angst owing to her position as well as the strong bond between her and her guardians, Shannon and Raquel, which gets trite.
Yet for all her angst, Pacifica is not an active character. Her guardians do all the work and later when they get separated she instantly finds a stranger that takes care of her and protects her, so that she's generally shown living a comfortable life. She never has to fight her own battles or be the main source of income. She cooks but she's bad at it. When she does laundry she makes her guardians do it too. Despite this she spends half of her screen time complaining to her guardians about being tired and hungry and generally acting like a pampered princess. After 24 episodes of getting cocooned by her guardians and allies that she somehow charismatically attracted, she's given a choice that would change the fate of the world.
The major reason why I can see people being absorbed by this series is because it utilizes a lot of emotional porn. Pacifica will angst by feeling guilty about being the scrapped princess despite it clearly not being her fault and despite being told that the prophecy is wrong repeatedly. And as I said, this angst is overblown when she constantly has people protecting her from physical harm, and she's never had to suffer much from self esteem issues caused by the world because she was raised in a loving family and is fed constant emotional support from her siblings and allies. In fact, she's shown to have an almost narcisstic bend to her; she beats up artists who don't draw her in a flattering way, glares at people for not liking her cooking, and says a guy is out of her league when he asks her out. Shannon's desire to protect her against the world at all costs is repeatedly emphasized so you can take in the emotional beauty of such a dynamic, but doing this doesn't reveal anything we didn't already know about the characters from the first episode. To keep this going,
(SPOILERS)
the show gives Pacifica amnesia, gets her another guardian, makes him sacrifice himself to protect her, and then gives her back her memories by having her remember Shannon's love for her.
(ENDSPOILERS)
All of which does nothing to further either character or develop the themes. Emotional porn 101. As such, character development across the board is miniscule or trivial. Other than people doing what they think is right by not killing the obviously innocent girl instead of listening to religious brainwashing, you have the standard "logical AI's develop emotion" trash.
Of course, the series also tackles major themes that might give the semblance of depth. I don't think so, and I'll explain possible thematic connections and why they don't work:
SPOILERS AHEAD
1) Discussion of fate/religious prophecy/destiny. First of all, it doesn't exactly discuss destiny because a prophecy that says something will happen is different from the thing factually happening. One of the central conflicts is whether or not to believe in the religious prophecy that says the scrapped princess will bring doom to the world, which makes sense in the medieval setting, where religion would play a large role in people's lives. However, the general problem of using this as a theme is that prophecies in stories almost never work. If the story says the prophecy is true, then there's nothing else to be said except maybe accept your fate. Usually though, if the prophecy is something negative, the story necessarily has to eventually reveal that the prophecy is false, in which case the only thing that can be said was that prophecies aren't always accurate so you can't base your actions entirely on them. Then the aesop is too simple and there's nothing to be learned. In the case of Scrapped Princess the prophecy is so at odds with common sense and morality that the obvious answer is that the prophecy is wrong, which was confirmed by the story about 11 episodes in. Pacifica is obviously a normal girl that has not shown the slightest tendency nor power of destroying the world and killing her would be cold blooded murder. It's like when people thought the world was going to end in 2012 and the only evidence was that the Mayan calendar ended on that day. The only lesson learned is that prophecies with little basis in reality are stupid, which the characters of Scrapped Princess learn upon meeting Pacifica. There's nothing about defying destiny here.
That's not to say the idea of prophecies or fate can't be used in storytelling at all. Rather, a prophecy or idea of fate has to be tied in a natural chain of causality such that things SEEM inevitable and thus characters actually have to grapple with the idea that most things are beyond their control, which definitely occurs in real life. In the case of Scrapped Princess, this would involve a Pacifica who manifests destructive powers and has trouble controlling her temper. That way, the prophecy would only be accentuating the human problem of not being able to control oneself and thus be doomed for a path of self-destruction. The idea of prophecy and fate would be relevant insofar as they describe how hopeless it can feel for someone to overcome their personal weaknesses. This would be similar to something like Lenny from Of Mice and Men, wherein the character seemed doomed from the very start. Done this way, the prophecy being proven wrong wouldn't be proving that it was a religious sham, BOOM all problems solved, but rather people worked their asses off to change the course of events from their most likely outcome. It would also make people's choice to believe in Pacifica much more significant, because they chose to see the good in a person who was so flawed, rather than make the obvious decision to not kill a perfectly normal girl.
2) Defying the gaslighting of religious belief--- if it was going for this, the series only touches upon this lightly, again owing to the fact that the characters decide to believe in Pacifica so easily. It doesn't explore the intense internal struggles that people who've grown up with a religion face when they start questioning that religion, and all the thoughts that go with it. In fact the series portrays religion in a pretty one-sided manner by making it the instrument of oppression on the human race. It doesn't offer any more depth than any one of those fake church episodes from episodic action adventures.
3) Humanity is too self destructive for its own good and should be controlled, freedom vs security--- the series is out of its depth when it touches on this subject. An alien race decides that humanity if left alone would destroy itself, so it fights a war with it. They fight a war to end all wars, basically. Then one of the humans decides the war will take too many more lives so she betrays the human race and gets it enclosed in a tightly controlled environment stuck in medieval times (apparently advanced technology is too dangerous). This is obviously too extreme of a solution that values security over a total lack of freedom. Furthermore the standard of living has generally increased since medieval times and international relations are much more heavily regulated now than it was then. But it still could have worked, if the series had explored the advantages of living in such a world weighed against the freedom or lack of freedom of the people living in it. Unfortunately, such worldbuilding is scarce. Instead, Pacifica gets the God of this enclosed world to free humanity after telling her that people should have the freedom to make their own choices and take responsibility for it, and God agrees just like that, as if she didn't have any basic historical knowledge about governance and this 16 year old girl who knows nothing provided this piece of wisdom to her. Basically, this series discusses the issue by swinging the pendulum between two extremes and thus produces no meaningful thematic exploration. Who would've guessed that humans should have free will, right?
ENDSPOILERS
That wraps up the themes. In the end, I don't think there is a single element that this show did well.