Basic Trope: A super-powered or super-intelligent character who could easily solve real problems within the world they live if they tried, but fail to do so.
Straight: Amazing Girl, a brilliant superhero, could theoretically cure cancer for those living in the universe she inhabits, but does not do so.
Exaggerated: Amazing Girl could cure all disease, ensure world peace, defeat all evil and create a utopia in her universe — and, in fact, everyone around her begs her to do so. She refuses to, instead using her powers for more trivial purposes.
Downplayed: Amazing Girl could cure the common cold, but she only gets around to creating a pill that'll relieve coughing.
Amazing Girl is from the future, and her bosses cannot let her technology become public, because of the great risk of it generating catastrophic changes in their timeline.
Although seemingly harmless and beneficial on the surfaces, the advances that Amazing Girl could bring to the world require massive sacrifice on an unthinkable scale or would ultimately produce worse problems and suffering further down the line, results that Amazing Girl refuses to risk.
Amazing Girl does not want the people of the world to become to dependent or reliant on her; she could solve every problem, but people would out of laziness start demanding that she solve every trivial difficulty that they themselves could easily resolve, which would distract her from the more difficult problems she faces.
Amazing Girl fears that interfering in society to such an extent would put her on a slippery slope that would lead to her putting herself above everyone as a totalitarian dictator.
Although Amazing Girl's powers and abilities are seemingly limitless, there are nevertheless certain limits which she has not managed to transcend.
Amazing Girl has to negotiate complex matters of international politics and diplomacy when dealing with some of these problems; world governments and authorities would react with unease and suspicion if Amazing Girl tried to interfere too closely in their affairs.
Or, actively, Amazing Girl simply gives the existing scientists a push so they can come up with solutions while she fights crime.
Amazing Girl's creations are tied to her life-force, or are otherwise restricted in such a way that only she can make them, and they will stop working when she dies.
If Amazing Girl's power is super-intelligence, no one can understand any of her attempts to explain her discoveries, or figure out how to work the technology she invents (it would be like trying to teach a chimpanzee how to perform brain surgery).
It could be even as simple as it merely being not feasible mass produce her inventions, and solving that is beyond Amazing Girl's abilities—she may, however, be leaving careful notes for when technology catches up enough.
Amazing Girl notes that some problems are too complex to cure; such as for example cancer or the common cold due to the nature of cancer or the fact that there is not just one virus that causes the Common Cold, and all of them mutate over time.
Amazing Girl is so afraid that some evil entity (a supervillain, rogue nation, etc.) will reverse-engineer her creations and either weaponize them or develop effective countermeasures that she doesn't even make the attempt. See also Played For Drama (below).
Amazing Girl is fully aware of her inventions' potential, and wants to mass produce them. But bringing any new product to market is a slow and often expensive process..
Amazing Girl lacks the resources to mass produce her inventions.
Amazing Girl has a mental disorder or disability that inhibits her mental ability/motivation to do so, in spite of her physical abilities.
Amazing Girl's inventions simply aren't useful on the mundane level; What use has the average household for a timeship or a spaceship?
Amazing Girl knows that providing her inventions would stunt mankind's true potential. If she were to provide them now technology would stagnate and that would lead to their extinction. Not interfering will cause much suffering for centuries but will make things far better on the millennium scale.
Amazing Girl actively devotes herself to solving everyday problems, with the intention of transforming her world into a utopia.
Amazing Girl slowly causes her inventions to progress society more.
Amazing Girl focuses on the everyday problems until events force her to re-purpose her tools. This leads her to getting involved in the traditional way.
Amazing Girl attempts to solve such problems despite her own intelligence and abilities being inadequate.
Awful Girl deliberately provides technology with the goal of worsening real life problems as a side effect.
Subverted: Amazing Girl initially refuses to meddle in 'everyday' concerns, but after much soul-searching changes her mind.
Doubly Subverted: Amazing Girl's efforts result in more harm than good, and she swears off such meddling in the future.
People begin demanding that Amazing Girl do ridiculously trivial things for them, such as mowing their lawn or giving them a backrub, and berate her when she refuses.
Every time Amazing Girl thinks about using her inventions to cure society's ills, a future version of herself appears warning of the Bad Future that will result from her actions. Amazing Girl always agrees not to do so, her future version always vanishes, and Amazing Girl always has trouble building a time machine.
Zig Zagged: Amazing Girl is selective in what she does and does not supply owing to her odd ethos. She refuses to provide conventional weaponry to others even in dire circumstances due to a belief that it is morally wrong to wield weapons not developed by oneself. She is however completely fine with biological weapons, oddly enough considering them pacifism. She does freely share her powerful clean and safe energy technology. While she gives cures to bacteria and viruses and cybernetic technology she considers fighting cancer in others a morally wrong interference in the collective of cells.
Amazing Girl is merely a Badass Normal or otherwise limited superhero; while she does have abilities that place her above most other people, she's by no means in a position where she's able to use her gifts to effect massive societal change on the scale this trope demands.
Alternately, she actually does use her abilities to bring about world peace, cure cancer, etc.
The creators do not want to offend people in the real world either suffering from these problems or actively attempting to solve them by suggesting that their suffering and efforts are trivial, and that only a fictional superhero can really solve these problems.
The creators do not want the world they are creating to differ that drastically from the real world in order to allow their readers to engage and identify with it, and mass societal change on a scale this trope suggests would make the world too different.
The creators feel that having Amazing Girl solve every problem would rob their story of drama.
Lampshaded: "For all the fighting you do, Amazing Girl, what good are you, really? When you can't stop the real suffering that these people you claim to love so much are going through?"
Invoked: The beings who granted Amazing Girl her powers established certain limits precisely so that she would not get too Drunk with Power and try solving problems she was not ready / able to solve.
Exploited: Amazing Girl's archenemy Elliot McWealthybucks is able to turn the public against her by pointing out all the problems she could have solved.
Defied: Amazing Girl actively attempts to solve everyday problems and make her world a better place.
Discussed: "Yeah, if Amazing Girl's so great, how come I don't see her dealing with the everyday crap you and me face on a regular basis?"
Conversed: "Why don't the superheroes in these books ever try to make a real difference?"
Amazing Girl's refusal to help solve everyday problems is merely indicative that she doesn't really care, and is no real hero; she focuses on the 'beat-something-up' problems because she's ultimately too cowardly and selfish to truly share her gifts where they'll do most good.
Alternatively, Amazing Girl decided, after one too many comments that she is useless, to indeed help with everyday problems, and things escalated until she was taking over the world.
Amazing Girl is tormented by guilt by her refusal or inability to use her gifts in such a fashion, and begins to question whether she is really any use at all.
She acquires a nemesis who was a law-abiding citizen until he went mad as a result of barely surviving a plague she could easily have prevented if she hadn't been so focussed on fighting crime. He's still sane enough to rub her nose in his origin story, and the number of infected who didn't survive.
Reconstructed: One of Amazing Girl's friends reminds her that she still makes a difference; whilst there are millions of doctors researching cures into cancer, only she is capable of dealing with the superpowered madmen, Evil Overlords and alien conquerors who threaten her world on a regular basis, and that 'no one can solve all the world's problems single-handedly'.
Played For Laughs: Amazing Girl isn't all there despite her talents. While her heroic inventions work perfectly fine, all of her attempts at converting her technology to civilian use end predictably in hilarious disaster. Other scientists interviewing her are stymied by her unique mind. Analyzing her inventions proves difficult due to being based on collections of kludges and hacks.
Played For Drama: One of the members of Amazing Girl's Rogues Gallery deliberately makes a point of weaponizing whatever she comes up with and using it to stigmatize the technology with the intent of forcing sweeping bans on things that could fix the worlds' problems.