One additional idea that comes to mind is the simple principle of hierarchy. The big NPCs have their own fish to fry and they can't be bothered with the small stuff.
As an example from real life, I work at a university. The university has a president, under whom serves the provost, under whom serve the deans of the colleges, under whom serve the department chairs within the various colleges, under whom serve the faculty.
As a faculty member I have to deal with the small stuff – problems in student attendance, exam performance, class participation, giving exams, writing lesson plans, etc. The president and provost don't write lessons plan for me. They've got their own level-12 problems. My dean doesn't get involved when one of my students doesn't come to class. He's got level-8 problems to resolve. My department chair doesn't grade my exams for me. She has level-4 issues to address. All that other stuff, that's low-level stuff I have to deal with.
I'm sure most people have a similar hierarchy in their jobs.
A hierarchical framework makes sense in a fantasy RPG world as well.
The queen of the realm just can't be concerned with a band of twenty goblins raiding some hamlet. She's dealing with the neighboring country's necromancer king who could send his thousands-strong undead army across the border at any moment. That's her job. Not swatting a handful of goblins.
So it's first-level PCs who get called on to defend the hamlet against that band of goblins. Why aren't higher-level adventurers solving the problem? Well, that band of fourth-level characters over there are too busy beating down a bunch of ogres terrorizing a larger town. Several miles away, a party of eighth-level characters are dealing with dragons that have been ravaging an entire county. And way down yonder, a tenth-level character has built his stronghold and is wrestling with domain-level concerns.
Granted, to make this model work logically, your world needs to be filled with evil and peril, in the same way our everyday jobs are filled with the mundane problems we all need to deal with. But, assuming your world is overflowing with evil and peril, a hierarchical view of the environment is one additional and simple means of answering the question of "why hasn't somebody already solved this problem?" The big NPCs are just too busy handling larger problems – and reaping commensurate rewards – to be able to deal with – or to be interested in – the small stuff. Those small matters are what first-level characters are for.