First off, the reason Ais is kept so far from the main story is because of advice given to the author by his editor. Oomori was warned that if Ais were to be closely involved in the story then Bell would never really be in danger and she would be able to resolve the conflicts. While not exactly false, it at best incomplete advice and at worst detrimental. Most editors or critics worth their salt are going to recognize if there is going to be a main love interest or hero/heroine complementary to the main character they must be closely involved with the story and often interacting with their counterpart.
The author's solution to this problem his editor pointed out was Sword Oratoria. While not necessarily a bad way to go about it, it fail badly in two aspects. One, the imperative of that Ais be pivotal to the main story and narrative. The second that Oomori told fans that the spinoff was not required reading when that in reality turned out to be completely false.
Also, Ais isn't going to be in season four. She played no part in it except for a SS when Bell is dreaming while trying to rest in the dungeon.
Ais does have a connection to the primary plot of the main series. Her past is tied to the big bad of the story. The foreshadowing for that is supposed to be in season three when Bell, Ais, and Hestia are in the village in the mountains, but it fails to convey her connection in the anime, I'll cover the limitations of adaptions later. By and large the anime actually does show a fair amount of what is in the main series about Ais, but again there is that limitations thing again.
You are right though a main heroine should be a major part of the story, and not in the way a McGuffin is, which is what Ais often is.
Getting in the actual story stuff now. Ais is the daughter of hero Albert Waldenstein and the great spirit Aria even though spirits cannot have children, who live 1000 years before the story begins. (Yes Ais is sixteen and no we don't know how Ais came to be born)
Her father was killed fighting the One Eyed Black Dragon along with his friends and allies while her mother seems to have been taken by it. This happened in front of a seven year old Ais. Understandably she was badly traumatized by this. She suffers from PTSD, depression, and emotional numbness. She was somehow found 1000 years latter by the Loki Familia who ended up as her defacto guardians. Unfortunately they let her focus on a quest for revenge failing to help her heal and move on with her life in time. Her trauma is why she has a blank face and struggles to understand social situation, the confused look she has sometimes, as well as has fits of extreme anger sometimes.
Years, her relationship with Riveria and her friends would help her heal a little. But she never really makes much progress until she meets Bell and he triggers something in her psyche. That is what was the start of her interest in him. Then later, desperate to become stronger to take back her mother she tried to learn the secret to Bell's lightning fast growth by training him. While she had an ulterior motive she did truly do her best to train him. Though she never learns anything about his growth other than he is chasing someone she does develop a true and genuine friendship with him which grows as the story progresses.
When Hestia is kidnapped by Rakia Ais goes after her for Bell's sake. During their time in the village Ais's reaction to the scales scare Bell. (The narrative puts an unusual amount of detail into it. That is called an irregular description, it is a method of foreshadowing). Later when Hestia is comforting Bell after Cam dies Ais is listening and calls to her mother. (Another small foreshadowing)
During the Xenos event having to fight Bell breaks her heart, but she like the rest of the world have only ever known monsters as creature who exist only to make them suffer and take those they love. Wiene shatters her understanding of the world and she has to try and figure out how to live with a new reality.
Throughout all of this Ais is slowly developing feelings for Bell which should eventually culminate in her falling in love with him.
I'll stop here on the story stuff.
Adaptions, I only got one episode into the second season before I decide I didn't like it so I can't fairly judge season two and three, and Sword Oratoria is genuinely a terrible adaption. However, I am going to staunchly disagree that season one is a bad adaption. It conveys most of the themes as best it can within the limitations of adapting the novel medium to visual medium.
In the literary medium author are limited to only what they can write and convey with language. Conversely that is also their greatest advantage. The narrative allows an author to directly convey what the want to readers with greater detail than can be done with visual mediums.
That is why much of the narrative in Danmachi is so harder to convey in the manga and anime, much of the most important parts of the story are conveyed in character narrative monologues and third person omniscient narration. Visual mediums pretty much have no good ways to really impart narrations that don't cause immersion problems. That is why you pretty much never see them in movies and tv shows. Ais is always blank faced, even when she is feeling bad. the only emotion she commonly expresses is anger.
The anime just went with it and kept the deadpan expression. In the Sword Oratoria manga Yagi took some pretty significant liberties to be able to show what Ais is feeling, sometimes having panels where something is only happening with Ais in her own mind while in the real world has something else going on.