This is effectively half of a two-part review. That's not with Season 2, although I'll be watching that next, but with a different show... that happened to have a near-identical premise and be shown in a similar timeslot on the same day. I gleefully watched them side by side... and got confused. You forget which plot points are from which show.
The other show is Chivalry of a Failed Knight, aka. Rakudai Kishi no Kyabarurii. Both shows conform to this template:
They're light novel adaptations set at Magical Duelling School, like Absolute Duo, The Irregular at Magic High School, etc. The hero is a paragon of humanity whose mild-mannered nature conceals staggering power beyond his peers! All the girls will flock to him (HAREM ALERT, HAREM ALERT), but of course his purity and innocence means he won't lay a finger on them! In reality he only has eyes for one girl, a pink-haired tsundere sword-wielding princess with magical fire powers who tries to kill him in ep.1 because he saw her in her underwear. Another key person in his life is his sister, associated with his painful past.
I'll leave out the lesser similarities, e.g. a supporting character who's a school journalist, a buxom, blonde and dangerous student council president, etc.
I found it quite interesting to compare the shows, like a laboratory experiment organised by the Gods of Anime. Chivalry of a Failed Knight has bolder plot developments, but it's also often a train wreck and personally I'd call The Asterisk War a much easier recommendation. It's immeasurably less eye-rolling. The plot's never driven by idiocy or genre convenience. The blow job it's giving its hero is fairly modest, while the supporting cast feel like real people and have brains.
Firstly, the hero, Ayato Amagiri. He has a personality! Being mild-mannered even under provocation is a trait he shares with Chivalry's Ikki, but the difference between them is that Ayato seems more like a human being. He's friendly. I liked him immediately. He walks up to angry people and resolves conflicts by discussing things. I like the simplicity with which he goes about things. Personally I prefer this as a character type to the Emotionally Distant Robot Who Probably Has Asperger's (Chivalry of a Failed Knight, The Irregular at Magic High School), even if the latter is theoretically more distinctive.
His princess, Julis-Alexia von Riessfelt, is likeable too. She's tsundere, yes, but in a relatable way. In ep.1 she's keeping everyone at arm's length. She's one of the strongest fighters at the school and something of a celebrity, but this is a pain in the neck (e.g. testosterone monsters demanding that she fight duel after duel with them) and she'd sooner not have to deal with this "friends" thing. Once Ayato's overcome her hostility, though, she's a nice girl. She'll always take you seriously and give you intelligent answers to your questions. You can have sensible conversations with her. She and Ayato make a good couple and I liked them.
As for the other girls, Claudia is a walking fanservice opportunity who can be, um, forward in how she approaches Ayato. I liked her a lot. She's basically benevolent, but with villainous undertones that she'll cheerfully mention as part of introducing herself to people. She actually says, "I'm a bit villainous." (She's not lying, either, and you really wouldn't want her magical powers.) Frankly, she's a bit unnerving under that buxom flirtatiousness. When Ayato flees in alarm from her sexual invitation in ep.3 (which might have been just teasing him anyway), that looked very sensible to me.
No other girl is making even that much running in the harem stakes. The others are either deadpan comedians who look about twelve (Saya) or sweet and genuinely that young (Kirin) and those two hook up together as a partnership anyway. That's just as a combat team for the Phoenix combat tournament, but that doesn't mean they don't get rather nice character development.
The most unrealistic thing about this series is the CGI animation in the Next Episode previews. What the hell is that? It's like a 1990s computer game. After that, the second most unrealistic thing is the weapon size. Saya's biggest guns are several times bigger than she is, although admittedly those are considered ridiculous even in-universe. (She uses them out of loyalty to her father, who's a mad weapons designer whose work is seen by everyone else as hopelessly impractical. They suit Saya's personality.) She has easily the silliest weapons, but Ayato's Ser-Vestra can grow pretty big too. That said, though, some of the magical weapons are intelligent and some of them are evil. There's one that turns its wielder into a vampire and that's not even the worst of them. I might prefer that to Claudia's Pan-Dora.
It's also set in a dystopian world. It's usually beneath the radar and you could be forgiven for not really registering it, but the world's being run by a mega-corporation, Integrity Enterprises Foundation, after an extinction-level event wiped out all the old governments. Entire countries have become slums and puppet monarchies have been installed, without even enough autonomy to provide social welfare. Integrity Enterprises doesn't like that sort of thing. It's less profitable. They even have a policy of mentally reprogramming their executives to erase all human desires and work only for the good of the corporation. However our heroes don't need to worry about all that. They're students at the famous tournament city of Asterisk, where life is good and anyone can become a celebrity... even if it's all for the sake of fighting live for the world's entertainment. Nonetheless there's also the question of what happened to Ayato's sister. She's disappeared. We still don't know what happened to her, but there probably isn't going to be an innocent explanation.
At the moment, though, the show's nice and usually light and entertaining. It's often funny. (The comedy robots I particularly liked.) Most of the characters have deeper stuff going on too and there are emotionally meaningful episodes that I rather liked, but we'll see how the dramatic side of things progresses in Season 2. I should warn you that plenty of people see this series as a by-the-numbers light novel adaptation with no surprises, but for me it works. I'm engaged by the characters. I'm fond of Ayato and Julis, Saya makes me laugh and Kirin is a sweetie. I also like the vampire, who gives us a satisfying season finale. I feel I can believe in these people, while furthermore the plotting has been allowed to retain a modicum of credibility. Ayato is capable of losing fights, for instance. As far I'm concerned, this is a solid story with likeable characters that's managed not to torpedo itself with light-novel-isms (c.f. Absolute Duo, Chivalry of a Failed Knight). I'm looking forward to Season 2.