It's clear with Shadowheart holding the mystery toy and how much Sharran stuff is in Grymforge and her scenes throughout EA, that she is the most important to the story. I mean, she will deliver the most content throughout the game.
Now that may not necessarily be true. She could be frontloaded and someone else has bigger importance in later acts unseen, but that is likely the reasoning.
I could imagine that every companion is in one way or another important- or in possession of something that is important - for the plot. Maybe our companions (and our Tav) were not randomly abducted by the mindflayers. This might also explain why almost everyone has a very epic backstory

- Gale's Netherese Magic Bomb, and being a former chosen of Mystra
- Shadowheart has the artefact. And since her memory had been wiped, we do not know anything about her past. Maybe there is also something important?
- Astarion's scars (that are definitely not a poem)
- Maybe Wyll's connection to Mizora, if she is not just some "random" cambion?
The only character where I do not see a connection yet is Lae'zel. It's funny that she is also the only one who does not seem to hide a secret

If there is indeed a connection, I am curious what it is that makes our Tav special.