The simple reason is because it's a game. The writers wanted your companions to have backstories and arcs that tie into the main story, including the locations you visit and characters you meet, and that all leads to Baldur's Gate.
I don't think it's really because of the Origin character thing, because normal Tav doesn't have or need a backstory that ties into the plot. So it would probably be much the same if they'd ditched the Origin character thing and just had them as companions to your Tav like other games, which is probably how most people play anyway. I'd guess it's more to do with the writers just wanting them to have a big part in the main story, where others might have given them less major roles or made their character arcs more separate from the main story.
Is it all a bit contrived? Sure, it was a design choice to put a bunch of characters together with strong existing connections to events.
Could they have made it all seem a bit more logical and less coincidental? Probably.
I think predestination is quite reasonable if you want an in universe explanation. In a world where Gods are definitely real and meddle in the affairs of mortals, it could well be that one or more higher powers has subtly nudged things along to get all the right people together for you to succeed. Possibly even the big cheese, Ao. Gandalf might say that they were all just meant to be together.
Personally, I like Lae'zel's character arc the most. Because she doesn't start with any big connection to the main events, she isn't special in any way, she's just a regular Githyanki soldier, but ends up being (or can be) super important to how the story plays out. Her arc is just developed throughout the game and doesn't rely on there being any big mystery around her.
