If you don't like the word "generic", call it rather a lack of specificity.
In terms of Origin runs where you get to see the most unique content and perspectives, I would order it as Karlach->Gale->Shadowheart->Astarion->Wyll->Lae'zel, although I think Wyll is a good Origin run simply because he's probably the least compelling companion, and his story is more interesting as the main protagonist.
I would have to agree with the people rating Lae'zel higher for unique content and perspectives. In fact, I think even
objectively she's inarguably above Wyll, like just literally looking at how much you can do/see as Wyll that you can't do normally. I also think Shadowheart is below Lae'zel for origin runs. Karlach has a big advantage in that she talks to herself, and whilst there's not a huge amount, there's enough to make it feel much more intentional. Gale is also very well-done. Whereas Wyll is one of those ones where it seems like they should, in theory have a unique perspective and content, but simply, factually, measurably, they do not. There are crazy numbers of places where Wyll should have Wyll-specific dialogue and reactions and he just doesn't. It's wild.
Wyll is a good Origin run simply because he's probably the least compelling companion, and his story is more interesting as the main protagonist.
In a sense, but that's kind of perverse to me. Because he's weak either way.
Nor does she feel unfinished, like our two poor horned companions.
Yeah and we know why, because Wyll's personality, voice actor and story were drastically re-worked around the same time as the other major story changes, or even a little later, and Karlach was literally just not finished until basically release and arguably not finished even then (c.f. them having to ending revisions specifically for her etc.). I think the big changes to Act 3 also probably messed with Karlach a fair bit. On the upside, I think the reason she talks to herself is that she was developed later, and that is actually an asset for Origin campaigns. I suspect that had the game remained in full development for another year before release, or had Larian done a DOS-style "Definitive Edition" for BG3 (which was pretty clearly intended prior to the messy break-up with WotC, indeed it would likely have been used to onboard staff for BG4 the DE was used for DOS1 and DOS2), we'd have got similar self-reflection in various forms for all the Origin characters.