It's definitely an interesting thought process. Personally I've not done fetch quests in my game much, except when the 'fetch' is for a macGuffin, I like to think out most things the player would do as a thing that surely the player character would do anyway. For instance, in early Intelligence: Rolly's belly is growling, and pep announces its market day, due to Rolly's appetite, Tristy, one of their newer friends, suggests swiping things without paying, it doesn't phase Pep incredibly much, but Rolly seems to disagree largely with the notion of stealing, Pep reminds rolly that if he wants to be able to eat enough to actually feel satisfied, this may be a lot more able to provide than simply eating the from the discarded plates of wasteful market-goers.
Pep states since he's got an element of stealth that he'll do it, although in the version where the story is revised, I have Tristy do it. So, yeah- it's a fetch quest, but with meaning.
A maze can often have a 'why' attached, a good example is a maze that holds no reason to be solved beyond just needing to be navigated to get from a to b. One good example of mine is in Intelligence, the Darkvoid, the maze isn't hard to get lost in, but doing so usually leads to treasure, and you'll get the layout pretty quickly, there's also a way to solve it on both routes. Getting all the sparkly treasure chests is the reason for the player to complete the maze, and most likely the characters, as well.
When a players and a characters goals are one, and the why means the same to player character in union, that's when you can create a real sense of establishment with your player to the characters.
Now, say a race, that can easily be done in a way that makes both the player and the character seek to win, if the character is a sort who is competitive- and the player's emotions come in line with theirs, especially if there's a character they are racing who they desire to outpass, this can become a mutally beneficial player-character experience. There are numerous examples of this in many big games, the first example that comes to my head is the race in Kingdom hearts 1 with Sora and Riku, who is immediately settled as the players rival, and is Sora's as well. So obviously, you don't wanna be second best, and any chance you can to become number one, you'll take.
As you yourself said:
Games involving connections is stirring understanding. It's a little abstract and difficult to talk about, but within the mental space the player is finding meaning.
To provide meaning for why both the characters and player may want to do something, the character you're playing must be fairly readable, because to relate to their wants and desires, the player must want and desire the same.
All of my games have a simple objective in the overall arc, and it's a prize that would be hard to say is undesirable.
Intelligence: Accomplishment
Hellcat: Understanding
Menagerie: Acceptance
Exile: Belonging
Perseverance Full Clearance: Liberation
Fantasia: Freedom
Boned: Survival
Crowfeast: Power
To give you a brief summary of each.
Intelligence: You start out as bottom feeders, feeling like the world is doing its best to make you into nothing, you have energy but nowhere to spend it. This changes and eventually you began to feel bursts of accomplishment, like player like characters.
Hellcat: At the beginning of the game, you're just chilling out round your house, walk outside and fall into a pit, next thing you know you're in Heldath, and having no understanding of how you got there, bit by piece you and the character, who knows as little as you do, begin to piece it together, and get invested in the new world and vy to understand it like the one before.
Menagerie: it starts with four outcasts, who have no real homes, even if they may have physical ones, Fyori doesn't belong, fatty is not at home, Gerald had never felt at home, and Spooky left his out of disgust and is now trying to find his own place in the universe, but he knows to do that, he'll needs go along with his mother's plan. All of them find acceptance in each other that they did not find from others, Spooky starts out as cold and demeaning, but quickly begins to warm up to and respect his peers, even Gerald- albeit in subtle ways. The others have similar situations. Fyori starts out feeling out in the cold and like she's agreed to help a cause with no stakes to her, however she quickly learns of a reason to aid, Fatty is one of the first really on board, and loves the thrill of adventure, and so happily volunteers, he also takes a liking to Spooky, since dwarves are hardwired to measure hostility as sass and enjoy sass immensely. Gerald is the most unsure for a while, but states that if there's a chance the world is in peril, then he'll act in the name of Yor, but promises Spooky no stay of execution one it's all over, as he deems Spooky a dangerous being. However, after Spooky lends him his time racer so he can go and do something foolish, he finds himself wondering why, Spooky states that there'd be no stopping him, so it's best he make it quick as he can, not to mention that gerald's experience may kill him, or may make him more competent, both are good things in the eyes of Spooky, Gerald accepts, After a while he begins to see Spooky is empathic, and just has trouble showing it, and while the two continue to bicker, it's done in a more friendly fashion.
Sorry that one went on a bit... NEXT!
Exile: Alien is sent to Earth for crimes against her own people, we are never told what these crimes are, but suffice it to say Lyza simply wants to find a place of belonging, she eventually finds it in helping a revolution overthrow the Australian monetarists and founding a new world order with the power of people at her side.
Perseverance Full Clearance: it's obvious from the first that living in a society run by the Naxonite Order is hellish, so throughout the game your goal is to liberate your country (britain), and then yourself in some way after Britain fails to be liberated.
Fantasia: Created for the sole purpose of being slaves, with a couple helping hands, the protagonists, Lumi, Lilac and Koko, seek out a way to ensure freedom, and for the cosmos to keep going on, they fight for Surreal Cosmic Progeny, for the freedom to be odd. For the right to be crazy, to teach even Goddesses that their rules will be defied if they are unreasonable enough.
Boned: Basically you're woken up from your kingly meditation by your mother, who states one must also practise food eating to live a happy fulfilled life, not long after, she asks the protags dad to help her grab a Deathly ichor, a needed ingredient, he however, is clearly too comfy to get out of his chair, using Richard's Kingly-knight-complex to his advantage, Richard's dad asks that he go on a quest to stop his most mild cold from getting less mild. The quest goes on many interesting twists, with lever puzzles that need to be solved to progress, it's a maze in a game, with a few very easy battles. only one of which you can lose. The goal being to obtain the deathly Ichor for a dish that will help you survive. Which is funny considering Richard is a skeleton, but that's never really gone into. In a flavour text he says food sticks to their ribs, this is likely meant to be comical nuance, but also might tie into some belief Skeletopians have. Food may work like magical nutrition, it's hard to say. Other skeletopians like Limbo seem to have no issue disregarding the rules of life when need be, but seeing as most skeletopians enjoy the pleasures of partying, it's likely they get some benefit from food.
Crowfeast: My, this is a good one to experiment with. In most games, the goal is to stop someone getting enough power to become unstoppable, however in crowfeast the magalomaniac is you, and the struggle for power is given to both the player and the player character, Mira. While her goal may be beneficial to the peoples of her homeworld Shale, she personally has her own motives, and the player shares in these, which they share in the most may well impact the route they take. Mira has only two combat abilities, Quell, and Execute. Quell is a silent KO, while execute is a Murder. If she quells all, she cannot allow Berk to feast on their misery, meaning her power never really grows. In this route, her main goal is to avenge her family's deaths and make some kind of understanding out of things.
Her Ravenous route, is quite different. She intends in this route to strike down anyone in her way, and absorb them for whatever they are worth, this is a route that rewards ruthlessness, as the more you kill, the more crazy your challenges get. Both however, are a power struggle, one is against those who wronged you, the other is against all who could potentially wrong you.
If you're a player who doesn't like killing people, and just getting done what needs be done, resolving things through diplomacy rather than violence, the Ghost Route is the ideal. But for those who would rather see Mira succeed to her fullest, and feel powerful alongside her, they can choose the Ravenous route, and while an official choice is never given, it becomes clear pretty quickly (before it's too late) that Mira is a tough pill to swallow when it comes to her more ravenous side, so you can choose to switcharoo if you don't want to get locked into one or the other.
Likewise, sparing people, or ghosting them, also isn't good for the player who likes to be in control, the only way they can be in control is via channeling themselves through Mira's ambition. In the Ghost route, Mira often gets cornered, and usually has to plead or excuse her way out of a situation, so if you don't like to conform, it will become clear pretty quickly which route is for you.
Anyway, hopefully this spiel resonated with you, somewhat~ I've naught else to show off yet.