Ok, so wall of text incoming, but bare with me. I agree with the complaint of the OP, themepark characters do detract from the game, for a number of reasons.
Firstly, even accepting the idea that a Nautaloid went past a number of cities and randomly abducted people, how likely is it that it grabbed a Priest of Shar, Mystra's Castoff with a magical timebomb, a Vampire Spawn, a Gith and someone with a pact with a demon. Obviously there were others and it wasn't just this group, but it seems unlikely from a narrative perspective to end up with this bunch of people to begin with. The priest of Shar and the Gith you can explain off, at a stretch, but beyond that you are stretching the limits of credibility and it detracts from the world's verisimilitude.
Secondly, by giving all of these companions, "epic backgrounds," it takes away from their personalities by making them more about insert_dramatic_plotline_here, than about them as an individual. They are merely a receptacle to explain a specific event, rather than a character. Gale is the weave guy, Astarion the vampire, The Gith is the Gith (I cannot even remember her name, that is how forgettable she is). You do not really think of them beyond their epic plotline, because it completely overshadows who they are.
Thirdly, the writers have failed heavily at the basic writing concept of, "show, don't tell," when it comes to characterizing the companions. Shadowheart is a very good example of this. Shadowheart is supposed to be a secretive priestess of Shar and yet how she behaves is completely at odds with her supposed backstory. If someone is supposed to be good at being secretive, they should be good at being secretive, they shouldn't be overtly "oh so mysterious and I refuse to tell you anything." The best way to keep a secret is to keep quiet about it, not draw attention to it (she shouldn't volunteer information about Shar unasked, only if a question is directed at her) and in the event that a question is directed at her, she should not outright lie about anything, just tell enough truth to keep people from being suspicious, whilst not enough for people to work things out. By trying to tell the audience that Shadowheart is secretive all the time, they have failed to make her secretive at all, thus undermining her character concept.
Fourthly, companions do not need to drown us in purple prose explaining who they are and what they are interested in. You can achieve a much better result, by providing less information, over a longer period of time, where it is appropriate. Have a companion interject a line or 2 when something upsets them or when they feel the need to give an opinion, don't give us 3 pages of text telling us their life story. An example I can give, from a book, which is very effective at creating memorable characters with a sparse use of text, would be the character Mercy from the books, The Black Company. When Mercy is first introduced, the only description of him the narrator gives is, "Mercy never grew up from being the kid who pulls the limbs off insects." It is a brief introduction and tells us enough to understand what type of character Mercy is. Then, throughout the book, our impression of the character is built upon by how he behaves. BG 3 does not do this and instead buries us in expository text for every companion we happen to collect.
As a result of these problems, as well as some others, I really do not like any of the companions in BG 3 at all and actively prefer to play the game solo.
With all of this being said, I do feel like this is a long time problem with RPGs and not just BG 3. I feel like the writers for games don't think they can hook people on their story if it is not a story with a chosen one saving the world on an epic adventure, complete with an entire squad of superheroes behind them in the party. There is one problem which I do not think the companions suffer from however, which a lot of companions in many games definitely do. The problem being, why are these people sticking together in the first place. Given that they all share a similar unfortunate turn of fate, it is in their best interest to stick together until their problem is resolved. Considering how long sticking together may take, they may have a genuine reason to stick together beyond this as well.
Minsc is, for me, the worst part of the BG games.
Minsc’s only fault is that his popularity made him a victim of fanfetishism.
I don't mind comic relief characters, if they are done well. I do not feel like minsc is an example of comic relief done well and as a result he grates on me. I dislike him because of the character execution, not because of any fetishism the community has added on since. A good example of comic relief characters would be Goblin and One-Eye from the above mentioned Black Company novels, who are much better than Minsc and I can actually enjoy them as characters. The humor they interject to the story helps to break up the tension and occasionally also advances the plot. It is also not completely overpowering to the point where you almost cannot distinguish between them and their antics, where as Minsc is almost entirely just the comic relief that he brings along.
I would argue the best executed character in BG 1 was actually Imoen. She was supposed to fill the role of Charnames close friend who is almost a sister and she does this well. There is a good reason for her to follow Charname out of Candlekeep, she has plenty of historic emotional investment to make her willing to follow you. She is also not a themepark character, who is fairly down to earth and has a fun personality. I think the 2nd game actually weakens her character a great deal, she never needed to be a bhaalspawn for the plot to carry through and adding that bit to the story only made it weaker overall.
