Well, it is very anime-ish, in terms of it's storytelling. It's got a healthy dose of over the top cringe dialogue. However, what makes it good, is that it's more than the sum of it's parts. It really does a great job of defining the characters, and connecting you to them, despite it's tropes.
Aside from that, the combat mechanics are some of the best you'll experience in a JRPG. It kind of turns the typical JRPG repetitive combat on it's head, and gives you more to think about than just gaining experience.
Overall, the whole experience just comes together beautifully, where you stop noticing it's faults. It's hard to explain properly, but it's just a really well put together experience. I put 120 hours into this bitch, and rarely did I ever feel fatigued. You'll grind, but it's fun. You'll roll your eyes a bit here and there at the story and dialogue, but eventually start to really care about what's going on. The gameplay loop is so damn good, that you think less and less about it's base level concepts, and just get swept away in it all.
In terms of your specific critique though, imagine a really bad B-movie that's just boring to sit through, and terrible all around, compared to a really good B-movie where you forgive it's faults, because it's just so damn entertaining and creative. I personally can't stand that typical anime cringe shit that I believe you're talking about, but with this, it got to a point where I never even thought about it, because I got swept up in the total package. The game is like a piece of coal, condensed and refined to a diamond. Give it a chance. You won't regret it.
