Throwing is quite broken in BG3, by virtue of the Tavern Brawler feat, as has been widely established. The question is:
Who from among our companions (or Tavs) should take on that role, assuming we want at least one character capable of using this broken feat? Karlach as a Barbarian (Berserker + Thief for the extra bonus action with Enraged Throw), Lae’zel as a Fighter (Eldritch Knight), or a Monk (Sina’zith being the default Monk hireling), given that Monks like to pick Tavern Brawler for increased damage on unarmed attacks? (Of course, if your Tav is a Barbarian, Fighter, or Monk, just insert them into this question.)
While there are enough regular spears to go around so that our characters won’t have to fight over them (and you can always pick them from another character’s inventory even mid-combat), the supporting gear for throwing, such as the Ring of Flinging, can of course only be worn by one character at the time — and Strength elixirs are finite, too.
I just saw a discussion in the YouTube comments about at which point Eldritch Knight outperforms Berserker/Thief — it seems to be fairly late in the game, when the Fighter has three regular attacks. So this seems to suggest Berserker-Thief is the wiser choice for the early game; however, if one is already used to this class combination by the time they reach the end game, would they really want to swap Karlach’s and Lae’zel’s roles at this point?
The Thrower usually keeps their distance (darling), so if Karlach is throwing from the back (as a Berserker), Lae’zel might be at the front tanking melee hits, likely as a Battlemaster. Conversely, if Lae’zel is throwing from the back (as an Eldritch Knight), Karlach is probably tanking as a Wildheart (Bear) Barbarian.
Since enemies like to go for characters with the lowest AC, having Karlach without armour be the tank may make more sense than Lae’zel, who is likely wearing the Adamantine Splint Armour or something similar. Karlach can also take the highest number of hits, since Barbarians are the only class with d12s as their hit-point dice. Eldritch Knight Lae’zel and Wildheart Karlach would also be the “canonical” options, as these are what the respective characters choose upon first reaching Level 3, unless the player changes it.
That said, whether this is “canon” is debatable, as Gale chooses Evocation Wizard by default when reaching Level Two, even though at the end of the game…
…Gale specialises in Illusion, if you choose the route where he becomes a professor.
The case for the Monk being the thrower, meanwhile, is that not only do they like to pick Tavern Brawler anyway — they also don’t like to remain in Melee range: They rush in, hit hard, then run away again, since despite having unarmoured defence similar to Barbarians (scaling with Wisdom instead of Constitution), they don’t have the same hit-point dice, and are therefore a lot squishier.
The Monk probably won’t want to multiclass into Barbarian for enraged throwing (even though I do like Minsc as a Berserker-Monk for roleplaying reasons), since Flurry of Blows will deal more damage with that same bonus action. However, the Monk could still use rush in, do Flurry of Blows, get out of melee range again, and then use their main actions for throwing attacks. Alternatively, if you do pick up Enraged Throw, you could make the target prone with a throw first, then have the Monk rush in and do Flurry of Blows with advantage.
So far, I’m mainly making Karlach the Throw-Berserker and Lae’zel the Battlemaster… but perhaps there are reasons for picking the “canon” versions, even in the early game, and swap those two roles around? 
