Knight-errants aren't a thing that actually existed in any accountable or sizeable fashion as "adventurers", especially not in medieval period. They didn't go around saving damsels and fighting evil, those are romanticised folk tales. There did exist lesser nobles without landed titles that served local gentry or lords, in hopes of getting landed titles for their service but that's about it. This was most common in Italy, especially northern Italy where it culminated into full blown mercenary companies lead by lesser nobility fighting each other at pay of landed lords. The term free lancer also refers to these type of people, who could afford arms and armour but didn't have lands to attend to.
There also did exists some nobles that went on what could be called adventures after discovery of Americas by Europeans. A lot of Spanish conquistadors were basically lesser nobility with either no land or low revenue land that hoped to go on adventuring and get rich. They would assemble few men, a ship and set sail for the "New World", sleeping in their armours and interacting with native people to find themselves a place. These would be more fitting to the type of adventuring that seems to be more common in cRPGs but even then it's a bit of a stretch. Especially since they were just expeditionary forces in the end, doing little more than fighting, scouting, exploring and acting as local officers.
However looking for the counter-part of adventurer in real world is a futile exercise because it doesn't really matter. The book Don Quixote criticises this romanticised and on the whole silly view of knights of old, and that book was written while New World was very much still active conflict zone and most of Africa was not touched by Europeans. So by value of playing a fictional character with a motivation for adventure, you are given a certain context for adventuring that you are going to have to take at face value. So I think it's better to accept that it's part of the setting and hope that the writers will make it internally consistent within that setting. I think it's better that way too because there is not much mercenaries did except fighting and looting, nor knight-errants who were officers for armies and would take part in battles, or as personal guards of lords. Those are better fitting in a strategy game or turn-based tactics game than a cRPG. They are not going to be anything more than background that gives the protagonist the context of their adventuring, as per character building or roleplaying, choice amongst many.
Ideally of course this invented context would be provided to the player with other motivations that personally involves your character, where quests you take interest you as more than just mere vehicle for giving you a direction to kill more goons to get paid but that's about quality of writing essentially. Setting can justify armed adventurers doing work that is not just killing people for money. A quest about delivering an amulet can be interesting, even though it's basically menial busywork, even though by merit of real world background it is not entirely logical. Meanwhile a quest about killing some bandits for just some coin can be very boring even if it befits an armed group of adventurers. So I think the critique shouldn't be about whether being a courier fits an armed adventure group but whether it's interesting, someway, to deliver that amulet and whether it aligns with general narrative direction of the game. This is I think best covered initially by letting main story of the game allow some side-stepping and perhaps even encouraging it as part of it, where the plot at points leaves MC to proceed at their own pace.
Knight-errants didn't save damsels or fight monsters in actual life, but boy, people sure dreamed they did, even back in historical times. We know this from reading all the fiction they wrote about it. It's a vital thread in Western literature through the ages, and that's how it eventually got spun into the cloth of CRPGs. Gygax didn't invent the adventurer. He took an existing trope and ran with it. Understanding the trope is key to understanding the role. Early Dungeons and Dragons pretty much assumed the player thought like a fantasy knight-errant. That's why the game was designed around treasure hunting, leveling, and combat. It sure as hell wasn't designed around dialogue, walls of text, or complex thematic explorations.
The problem with modern CRPG developers is that they can't, at a basic level, free themselves from this legacy, yet that doesn't stop them from trying. As other people have put it, CRPGs started off as attempts at emulating the classic pen and paper experience in a digital format. That's still what they are, when it comes to overall game play and structure. The whole concept of main quests, side quests, dungeon crawls, equipment, character progression... Those are all based on either Dungeons and Dragons or similar systems. As long as that remains the case, you can't get away from the principle motif of the game world, which is that of wandering parties of adventurers killing monsters, completing quests, and hunting equipment for the sake of
self advancement or an excuse that requires it. Trying to avoid this in your story telling or world building is like trying to avoid the reason your game exists.
How might a completely different system look like? Well, it'd look like a separate genre, altogether. A game in which survival is the primary motivation, would probably look a lot more like Rust or The Forest. A game in which you always had a mission to complete, would probably be more similar to action games. Indeed, that's one of the observations I made about Nier: Automata - most of the side quests in that game felt as poorly motivated as they do in Pillars of Eternity - even though they were thematically relevant - and the game would've been better off without leveling mechanics. It goes back to trying to do too much within the confines of the genre.
So to get back to the argument: a quest about delivering an amulet can be interesting content, but for it to fit the logic of the game world,
it has to be motivated within the context of the adventuring trope. Otherwise, it'll always feel disconnected and relatively out of place. Fortunately, most people are willing to forgive flaws of this sort, or in Jeff's words, they're willing to tolerate the story to get to the game play. Had that not been the case, Pillars of Eternity would've never sold a million copies.
But since we are talking about this specific flaw, I just have to keep on stressing that the reason it exists is because developers either cannot or refuse to grasp the central importance of the adventuring trope in CRPGs. For the typical CRPG game structure to feel properly motivated, the player either has to be driven by self advancement, or the side quests have to be requirements for the main quest... And in that case they aren't, to be a dick about it, side quests.