Forget this show exists, and imagine I'm pitching you a new story I want to write:
"A heartwarming comedy about a low-confidence student who befriends his classmate with crippling social anxiety. Everyone thinks they're just unfriendly or quiet, but really they're incredibly anxious but desperately want to make friends. Slowly he helps them come out of their shell and learn to socialize"
Now you're thinking, maybe it's this nerdy guy who gets bullied, or a chubby person who's extremely self-conscious about their weight. It's a wholesome story where they help each other develop confidence and integrate into normal social life.
Now I give you the final detail: it's an anime. Now it all falls into place. The awkward classmate? Big boobs, hottest girl in school. The main character? Completely generic self-insert male. Does she actually end up making friends? Maybe like two, but it's a gay guy or something (anime still does not understand trans people), and some social outcast girl, so we don't actually have to worry that Komi-san will outgrow the main character.
That's the problem I have with this show: it presents itself as this wholesome story about helping a poor girl who just wants to make friends, while it actually has no intentions of making her any less reliant on Tadano's support. Because it's really a self-insert fantasy about taking care of a helpless, beautiful girl. If she actually made progress and learned how to talk to people, she wouldn't need Tadano (our self-insert) anymore.
When you look at it this way, all the contrivances become impossible to ignore. How is that Komi-san has gone ~16 years of her life without ANYONE noticing her anxiety, even though Tadano figured it out in 5 minutes? Because we're supposed to feel special when we project ourselves onto Tadano: only a down-to-earth guy who doesn't care about popularity (just like you!) would be able to see her as a person. Somehow Tadano is the only decent human being in the entire school, and the anime expects us not to question that, because that's how it assumes we think about ourselves.
Literally everyone else in the school, even the teachers, have to act like they're from another planet in order to maintain this fantasy. Every guy is so obsessed with Komi that they won't let each other interact with her, every girl worships Komi so much that they don't feel worthy to speak to her, and even the adults rationalize her antisocial behavior as some kind of enlightened nobility.
Now, I know what you might be thinking, "but that's the joke! It's ironic that everyone thinks she's perfect!" And yes, it is humorous for a bit, but the joke overstays its welcome. Why keep doing the exact same joke episode after episode, stretching its believability way beyond the breaking point, when all it does it prevent the story from making any progress? Why not let Komi break out of her shell, let the students realize she's not some superhuman goddess, and let her actually start speaking to her classmates and making friends?
Because, that would ruin the fantasy. If Komi-san learns to speak, suddenly she doesn't need Tadano anymore. She's the most desired girl in school, she'll have a hundred friends instantly. She'll have a dozen boys trying to date her. Tadano won't be able to maintain his monopoly over her, because his entire character is that he's a mediocre guy. The anime is forced to keep Komi isolated, only give her one or two friends who are carefully established to be incapable as romantic rivals, so that we can keep her to ourselves.
That's why I don't like Komi-san (the show). The need to maintain a wish fulfillment, self-insert, power fantasy poisons every joke, every interaction. The humor is alright, the characters are cute, it's an exciting premise, but because its priorities are so clear, any hope of it turning into a genuinely heartwarming story are gone. And just to prove my point MINOR SPOILER: I skimmed ahead to chapter 200 of the manga and Komi-san is still not speaking, while Tadano has to supervise all of her social interaction.