I consider sidebar interactions like that to be part of the immersive exploration of the setting, so to me it adds to the experience. Not everything has to be directly related to the main story, and those little bits of lore help fill out the feel of the place. That being said, lengthy exposition tend to be a drag on the game's pacing, so I think they should be edited down.
Let me explain with more elaborate hypothetical example to give you a better feeling about what I mean
You want to solve certain puzzle in the game to discover new location, so you know from some source that king might know the answer. You step into nearest Tavern and ask bartender if he knows where can you find the king.
Bartender answers with a question. Did you see that blacksmith in front of the market which is few meters away from the church that is located near barber shop ? Well there lives a smith who was born outside of this village, he once crafted a powerful weapon that helped our current king slay the dragon. This weapon was made of special crystal, which can be only obtained from the mine guarded by the powerful golems. To kill golems you will need sacred water, from the well near the central market in elf village, but to enter the village you first need to undergo special ritual <you keep reading and you keep reading> After half an hour you know the whole story of this empire, and you ask again. But can you tell me where is the king ? The bartender answers. The king ? Ah king.. well I don't know that.
I love reading fantasy books, stories and to me, the whole story in the game is what makes game interesting. I really don't care as much about game spells, classes, weapons and the most I don't enjoy clicking to kill 10th time the same monster or saving the princess. I would like to feel the character, understand them, grow into being part of the party and when game ends, I would like to remember locations, music, characters and miss them