It's a pretty boy show. The only exception is the title character, who looks like a child and could just as easily have been the Token Female Protagonist in a reverse-harem show. (However such protagonists tend to be bland, which Haine isn't.)
(a) Haine has four princes to teach. They're all airheaded pretty boys! (Even the one who's a book genius is still an idiot with the common sense of a bluebottle trying to fly through a window pane.)
(b) Their father, the king, is just as young and beautiful! He looks the same age as his sons. (This is even lampshaded in ep.6, when he goes to work in a cafe and has all the girls swooning. "He's older than he looks, you know!" protests his son.)
(c) Even the male villain is as pretty as everyone else. (He's not a particularly important character, though. You could remove him from the show with very little effort.)
What's more, the princes are Stupid But Adorable to a degree that can occasionally be eye-rolling. ("Stupid" is a slightly harsh word, but I'd have been flattering them if I settled for "silly" and you wouldn't let most of them out on their own.) 1. Leonhard is so allergic to schoolwork that he can't calculate one plus one, despite being almost an adult. 2. Bruno will end up hero-worshipping Haine so much that he's like a duckling with its mother. 3. Kai's so bad at social interaction that you'd swear he's retarded. (The show wants us to believe that strangers find him scary, but no. He delivers his dialogue in the manner of someone who can repel hostile psychic powers because he's got the mind of a two-year-old.) 4. Licht is the only one you'd expect to survive if dumped into the real world, but he acts and talks like an empty-headed flirt.
I don't mind this series, but it can be silly to the point where I'd occasionally get a bit impatient with it. The silly cleaning in ep.10 might test your patience, as might the half-wittedness when the princes go into town in ep.4. (Why does no one ever recognise them? Well, this looks like an anime equivalent of the Habsburg Empire, so we're looking at 19th century newspapers and no paparazzi or social media. People might not know what their king looked like.) However I'm not the target audience for Pretty Boy Anime and I'd have probably been more tolerant had the show been all-female rather than all-male. (There are occasional maids and so on, but they're only ever cameos.)
That said, though, what's good about this anime?
Haine's quite fun. He's the opposite of all these light-headed boys. He's a dour little taskmaster who never smiles, demolishes every task with po-faced seriousness and is brutally honest with everyone. This makes him quite an amusing foil for his silly students. He gets annoyed when people assume he's a child and he has significant backstory with the king, which we eventually learn in the surprisingly good ep.11. He's also a good and very serious teacher, which I appreciated. (I'm mildly allergic to shows about a teacher who can't be bothered to teach, although there are glorious exceptions like GTO.)
The boys all get significant character development. They learn from Haine. They start out as over-privileged brats with severe personality issues and a hatred of all teachers, courtesy of the string of inadequates they've been given until now. By the end of the series, they've acknowledged their problems and taken significant steps in overcoming them.
It's also amusing, if you're in the mood.
Overall, it's okay. I watched it. It wasn't a slog, even if it was never top of my list. Right now, I've found myself watching a queue of shows that don't match my usual tastes, with this, Fate/Apocrypha and Dakaretai Otoko 1-ni Odosarete Imasu. I wasn't racing to watch it, but I plodded through quietly enough and was usually okay with it. It didn't make me fast-forward or anything. It's a light-ish, silly-ish bit of fluff with cute boys being cute, with the twist that they're princes. (Ep.7 does a version of the end credits with the voice cast performing the song as an idol dance routine.) At the same time, though, it has enough semi-drama and character development that you can follow it without having to wear your Irony Head. Haine's teaching role is taken seriously and he does help the boys grow as people. I didn't keep the episodes after I'd finished and I wouldn't really recommend this to anyone who doesn't already watch Pretty Boy Anime, but it's not too bad.