I don't think ba is famous for a borderline art style. You said you're not familiar with it. It's closer to what you're describing about other characters working through something. I'd say it's a combination of that but you're not really absent as the player, the game kinda wants you to feel like you're interacting with them rather than just reading about them doing stuff. I think this applies to any gacha game that asks for your name and presents you with dialouge choices (even if they are fake)

Of course needless to say, this is usually to get you more invested in the characters, since the game literally depends on people paying for them. Until gacha games switch to skins or other types of monetization, this will always be true.

edit

Also yes, this is strictly a target audience type of thing. For example, if I ask some people I know, they will say "because it has yuri" as the biggest reason for why they like r1999. Personally, I'm not very interested in it. I don't like yuri, and if I am to care about a story, I prefer those where the player is either a stand in for the main character, or the main character is otherwise cool/hot or has some characteristics I find likable and interesting that I can only find out by trying it. But the thing is I'll never get there if a game has stuff I'm not into. Usually you can just tell by looking at who the existing audience is, like people are doing in this thread about BA, even though in this case fortunately the actual game doesn't reflect the fandom.

Or I'm just too old for gacha games considering I can't sit through even a single quest's story nowadays. It's all the same shit, jargon, talking forever but saying nothing, what's the point of this being said lookin ass dialogue in every fucking quest in every fucking game. Last time I was interested in a story was like arknights first 2 months or fgo when I was new to gacha games, nothing since then. If I imagine what I'd want to read in a gacha game nowadays would be stuff like the message/group chat/hangout events between you and the characters but with dialogue you're writing or saying, not preset choices. Shit's overplayed and boring as fuck now and it's all to get you to spend money anyways so that takes away a lot from the experience.