I'd say you're given the opposite of solid reasons to explore. Look at the whole Zorru thing, Lae'zel gets the patrol's position straight up pointed to her on her map. Why. Just keep it vague in dialogue, highlight the whole area instead of giving me a pointer in gameplay, and suddenly i'm no longer going out of my way to get Karlach's quest.
Ethel and the east section are a bit better because one could naturally stumble on her and the brothers while trying to avoid the goblin ambush in the settlement, but the only real story reason to venture that way, other than playing an entirely trusting character who confides in random old women, is the whole Khaga situation, which isn't really all that overt.
As for the Underdark, i think that's just iffy level design. Why place the cool optional area (tower) in the easily accessible lower left corner, the map's exit (duergars and boat) in the middle, and the only piece of story-relevant content, which also gives a really compelling reason to explore the cool option area, in the upper parts (myconid village and 'good' mindflayer).
Obviously none of the above would be issues if it wasn't for the plot's underlying urgency, and hell if i tune that big detail out the exploration feels very BG-like especially in the Underdark. But since urgency is a thing, i believe that approach should be most defintely sacrificed for a cleaner and more streamlined level design, at least until we're straight up told the tadpoles won't act out at any moment.
