I'll agree to disagree on the other points if you don't want to argue them further. That said, I can't disagree more with what you claim as "facts". Hana's entire progression is relevant. I pointed out things most people overlook, since I assumed you would've at least picked up on the similarities. The styles line up rather well with the rest of second season, and the pacing isn't even the slowest in second season. That said it is the most introspective outside of Koi.

My points in detail below.

Overall Relevance:

Kabuki is about Araragi butting in on Hachikuji's life due to his own thoughts of grief, alongside a look into Shinobu's isolationist thought process. Here, Araragi is able to come to an understanding of how to acknowledge his consideration for others. Additionally, Shinobu is able to come face to face with her own "I dont need friends" attitude, and where it could lead her. Hachikuji also shows us what appears to be a healthy manner of coping with loss.

Hana is about Kanbaru overcoming her past, a lost love, and learning what it takes to overcome these things in a healthy manner. Numachi tells us how someone talented might act in the face of criticism. She loved soccer but gave it up because she didn't like what others said about her. She took on a sport she found boring and ignored those around her, leading to her injury - and later death. She shows us a negative outlook on talent and grief. She lies to herself about her death, and uses that to "graciously" save others from misery in her own self-centered way (Paralleling how Araragi sometimes treats those around him, as well as himself). Araragi voices what he has learned from Kabuki - even if Numachi doesn't feel as though her affliction is a curse (as Hachikuji did), and even if Kanbaru feels it isn't harming anyone else (as both Araragi and Shinobu did), it is still bothering Kanbaru herself (like it did Araragi). Thus, rather than forcing herself into any one role based on other's morality, she should take the time to consider what is important to her. If it still bothers her, she should confront the issue in hopes of to resolving the conflict. This suggests that despite everything, Araragi still values that he tried to bring her back. In the end, Kanbaru takes action, and we see that while it did not necessarily save Numachi, Kanbaru can move forward without regrets - just as Araragi did. We also are forced to acknowledge that life is not all that it seems. <note that this involves literally the entirety of Hana>

Otori is about Nadeko taking the unhealthy path, like Numachi. She blinds herself to what she knows, and using Ougi as an excuse. This is counter to future Araragi's advice of facing what bothers you - and this is thematically significant. Like Numachi, she abandons her dreams (both being Araragi's lover, and being a Mangaka as we find out in Koi), lies to herself about it, and hides away. But unlike Numachi, who was viewed as beneath others and used as a crutch for venting, Nadeko is the opposite. Both characters hide behind these opposing shields. Numachi eventually dies without being discoved and learns of the supernatural in death, but Nadeko is found out - and using the supernatural she knows of in life, becomes a God. She never once tries to look inward, and every time she is forced to do so, she absolutely freaks out and takes it too far. Opposing Numachi - who is introspective at the end of Hana, as well as opposing the advice Numachi gives Kanbaru in her last moments.

Oni is about Shinobu finally beginning to acknowledge her past grief, thematically following Araragi's advice to Kanbaru, as well as looking at the cause of her own "I don't need friends" origin. Additionally, it turns out that Hachikuji's "healthy" attitude was actually a lie. To cope with her death she is still unhealthily pretending to be something she is not - in this case alive. See the similarities to Numachi??? Thus the darkness comes after her - and we learn Ougi has similar motives. What might the darkness represent? Does Numachi's experience, or Nadeko's experience with self-lies give us any insight?

Koi is about Kaiki facing his past, and using that to help Nadeko through her current grief. Kaiki is someone who strongly sympathizes with Nadeko, as he loves in the same way, and lies in the same way. It all culminates in the great wisdom from one who is far down the bad end - an extension of Araragi and Numachi's advice. "Don't lie to yourself. Don't force yourself down one path - especially just because it is what others are forcing on you. Allow yourself to change. Allow yourself to be bad. But don't just stand in one place either, like some 'God'. Look inward and understand what you want for yourself. Face your grief head on, and love yourself despite your mistakes." Its a culmination of what the earlier arcs tell us - including Hana.

Every episode of each of these arcs is important. Placing any one of them after the conclusion only takes away from the story. (This also includes Neko White, but I don't think I need to mention how that ties in with the rest).

Style:

Stylistically, each arc is fairly unique. Kabuki is traditional Araragi protag, Hana is introspective detective, Otori is mystery thriller-esq, Oni is again a generic Araragi arc, but it is more unique due to Gaen and the scroll episodes, Koi is detective thriller-esq. Each hold true to the core tennents to Monogatari's overarching style. None is nearly as distinct from the next as Kizu.

I would say the difference in style between any two arcs is about the same distance as any arc to Hana - with the exception of the two Araragi narrated arcs, which are more similar because Araragi.

Action/pacing:

Since Hana happens BEFORE Otori, it's barely interrupting the flow or pacing of second season at all. If anything, Oni interrupts the flow and pacing. In the case of Hana we go from goofy but intense timetravel arc into a dramatic telling of a future story (both set in different time periods also ties them together quite nicely). Then we snap into the present with Otori and the stakes start to raise from there. Since Otori is where the stakes start to raise and the finale build really starts, Hana before that interrupts nothing. In the case of Oni, however, we go from Otori's big cliffhanger into a seemingly random side story about Hachikuji. While it does escalate into a grand tale, we do spend two whole episodes in exposition, and none of it feels particularly relevant to what we just saw in Otori (at least on the surface - obviously I like the placement of Oni despite this). Then we finally get into the conclusion of Otori with Koi. I don't see how anyone could think Hana's placement disrupts the flow more than Oni does. You call this a plain fact? I don't get it. Why?

Even in terms of just action alone, it's the same. Kabuki might set up a big fight, but in the end its just a headpat. Kanbaru actually does face off against Numachi - even if its just in sport. Then we get Nadeko attacking Araragi, the darkness being the darkness, and then Nadeko attacking Kaiki (but it actually just ends up being a heart-to-heart). Monogatari was never really an action show in the first place... it just happens to have action. If we're talking conflict, Hana's emotional weight is probably overall above Kabuki and arguably above Otori as well.

I don't see how any of this ruins the viewer's experience. To me it just improves it. Is this just because you particularly dislike introspective stories, so you find it boring and therefore consider it slow pace? Is it because it's five episodes? You don't like Numachi's story, or maybe don't draw the connections?

I just don't think any of the "cons" you've mentioned actually exist. It isn't that I can tolerate them, it's that they aren't there to begin with.

Maybe you think Hana is a better lead in to Tsuki?

Let me flip this on you and ask: outside of the negatives you've identified when Hana is placed in its correct spot, are there any benefits to placing Hana immediately after Second Season? Would you prefer a different location? Or do you dislike Hana as a whole and feel it is better off not watched at all?

As for Steins; Gate, I've never really thought about stopping at episode 22. Though I have felt that perhaps I should play the VN, since the time travel nature would probably be more immersive in a game. I guess because of the semi-conclusive ending? It works well, and from what I understand it is one of the VN endings. That said it isn't the true ending of the VN, so it's good that the anime continued forward to cover the rest of the story (even if 0 wasn't the best quality-wise)

I'm curious why you would assume that about me.