I've beaten the game using nothing but 4 gnome barbarians. So, no. You don't need casters at all. Just learn how to throw.
Throw stuff at casters?
Easily. The game isn't very difficult unless you're on an honor run, you shouldn't even need any consumables to get through it, just bash your head against the wall and it'll break easy enough.
Oh wait, you ARE talking about the honor mode run. You should still be fine so long as you know what's coming up. I've done a couple of runs and I've never even touched haste, or elixirs, or speed potions. Honestly I feel like the first act of the game is hardest in honor. Usually much smoother sailing once you're established and geared up a bit, as opposed to one or two bad rolls potentially wiping your whole team.
Some spells are annoying but usually not something you can't outtank/outheal. Just give yourself and Lae'zel tons of running distance and focus down the biggest threats first.
Do you know if you will go half illithid? That should give you even more movement and one counter-spell per (short?) rest.
I'm definitely using my parasite powers, I'll have to look for the counterspell there, I'm sorta low on worms at the moment though.
Baldur’s Gate 3 is a story-rich, party-based RPG set in the universe of Dungeons & Dragons, where your choices shape a tale of fellowship and betrayal, survival and sacrifice, and the lure of absolute power. (Website)
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