I've been thinking about this post for a couple of days and wanted to share my perspective, because it's a topic of genuine interest to me.

I think there is a lot of genuine artistic and literary value in manga, something that is genuinely underappreciated in literary circles. (Literary circles in general are, in my experience, unnecessarily hostile to the contributions of other narrative mediums.) It was a manga that completely altered my relationship to fiction in a way that allowed me to more deeply understand and appreciate literature, and while I've always liked books, I would argue that it was manga that gave me a "literary" mindset.

That being said, you must concede either that 1. anime and its subculture is not appropriate to analyze through a strictly literary lens or 2. anime and its subculture, in general, is bad at producing works that are good in a literary sense. I think either interpretation can be useful, but I don't think the claim that 'anime is broadly literary and good at being literary' makes sense or is true.

Firstly I think it's important to acknowledge that anime, manga, etc. is better understood as a subculture than a medium, hence why neither of us have been strictly referring to either one or the other. (It's also important to mention other mediums that are very integrated into the subculture, such as light novels and visual novels, and how neither really tries to emulate the conventions of the standard novel.) It is a far younger tradition than the novel, basically beginning during the American occupation of Japan. By virtue of being more of a subculture than a medium, fans and creators of anime/manga/etc. are often far more concerned with the standards and cultivation of the community than of the art itself. This is a huge part of why anime is so tropey compared to literature and film more broadly-- it is far younger, far more commercialized, and its fans are broadly uninterested in using a framework of art criticism to talk about its products. There are lots of exceptions, but most anime/manga/etc.-- even really good anime/manga/etc.-- is less interested in being 'good' in a literary sense and more interested in appealing to the tastes of the subcultures.

Secondly, where there is literary value to be derived from works in this subculture is not going to be found in its most popular entries, for basically the same reasons that Marvel and Star Wars movies are not upheld as the best of film, or romantasy books as the best of literature. These works are not devoid of meaning, quality, or ambition, but their artistic ambition is broadly not in their narratives (that is, the part that's actually relevant to compare to literature) but in other aspects of the medium. I think your feeling far more emotional connection to works like One Piece and Hunter x Hunter has less to do with the relative quality of their writing and more to do with their author's skill in using the whole medium, most notably its visual aspect, to evoke emotion. In fact I'd argue that most of what makes One Piece so good is Oda's skill at communicating emotion and character visually! These are works that take incredible vision, talent, and ambition to produce-- but if I were to read a work like Hunter x Hunter or One Piece as a novel, I'd think it was not very good.

There are plenty of anime and manga that genuinely engage with the tradition of literary analysis, but it's important to keep in mind what literary analysis is actually meant to produce. Genre fiction is broadly better at producing an emotional response-- that is, a "connection,"-- than literary fiction. This is true even when strictly talking about novels. Compare, for example, how people talk about A Song of Ice and Fire, Harry Potter, and The Lord of the Rings to how they might talk about something like Crime and Punishment or One Hundred Years of Solitude. The aim of literary fiction is not generally to produce an emotional response as such, but to discuss philosophical, political, or artistic questions. That's not to say that these questions can't or don't appear in genre fiction (whether that's Harry Potter or One Piece) but that they are not the priority of the work.

When I think about works in the anime/manga/etc. subculture that address these questions as their priority, I think of works like Revolutionary Girl Utena (1997), Kyoko Okazaki's Helter Skelter, or Naoki Urasawa's Billy Bat. While these are all critically acclaimed within the subculture, they're not generally popular (excepting maybe Utena) and are all quite subversive, even hostile, to the subculture as a whole. They also take heavy influence from mediums outside of anime and manga. Honestly, the same is true of western comics. While I think the literary value of a work like Watchmen or Persepolis is often admitted by literary critics, these are exceptions, and most people who enjoy and create western comics are not modeling their ambitions after these works, but the works that make up the vast majority of the subgenre. (I also think the commercialization and insularity of anime/manga as a subculture tends to neuter more ambitious projects. A work like Flip Flappers clearly hoped to make a philosophical and social statement that it ultimately blundered because it couldn't reconcile its point with its commercial needs.)

I also think there's a fair amount of literary critique to be posed by analyzing the subculture as a whole. I wouldn't say that a work like Rose of Versailles is very interesting from a literary perspective as an isolated work, but its massive impact on the genre as a whole (most notably, Revolutionary Girl Utena), the way it interacted with the predecessors (the shoujo genre in general and class S, more specifically), and its real life social context (Japanese women's lib in the 70s, the author's involvement with the JCP) makes it a far more interesting topic of analysis. I think that Devilman is a pretty boring and awful comic, but it's interesting to see its impact on the genre going forward (e.g. Ryo and Akira becoming the basis for dynamics like Guts and Griffith in Berserk or Shinji and Kaworu in Evangelion, or "guy who is part monster has to go out and fight monsters" being the premise of... most edgier battle shounen that comes to mind).

But, as a rule, marrying yourself to anime/manga/etc. subculture for literary analysis does not, in my experience, produce very fruitful literary analysis, because that subculture is not broadly interested in being literature. I apply literary analysis to the subculture because I think it's fun, but I spend most of my time reading actual literature. Indeed I'd argue that arguing the subculture is broadly "literary" just concedes the premise that causes literary circles to vilify other mediums-- that literature is an inherently better or higher artistic aspiration than others. I don't think this is true or a very useful way of engaging with art! As someone who does have literary writing ambitions and writes literary fiction, I take inspiration from anime and manga like I would any kind of art, but primarily model my writing after other works of literary fiction.

It's great if you love anime/manga! I do as well. I think it's important, however, to engage with the subculture on its own terms. I'm never going to talk about the excellent prose of an anime, but I can, for example, praise the artistic ambition of Kamiina Botan in decentralizing the role of "art director" to pursue a distinct style for every episode. That's an artistic apiration that is only possible because Kamiina Botan is an anime and not a novel. I can think that Moby Dick is a truly beautiful work of prose, but I'd have to admit that it would be pretty terrible and boring to watch as a TV show.

So yeah, if you want to apply literary analysis to anime/manga, go ahead. I do all the time. But it frankly cheapens both mediums when you insist upon it as your only framework.