Why a high-level character cannot stop a goblin invasion on its own? First of all, what kind of goblin invasion? A few thousand strong host in the medieval style could be definitely smashed by a high level character - at least by a druid, who is the best at mass destruction.
Here is a funny - and well written - description of a high level druid destroying an army.
http://www.enworld.org/forum/story-hour ... ost1029552
(That story is very good in general - it is the best example of pastiche in Jack Vance's style I came across).
Now let's consider why such things do not happen every day. First of all, I refuse to take Forgotten Realms into account - it was never designed for D&D, and is so full of special rules and exceptions that it is simply a bad example.
In addition I know that in D&D there are infinite loops and other ways for characters to gain unlimited power.
But I am assuming well-written rules, in which high level characters are powerful, but finitely powerful.
This is what we (ie Frank) are trying to do here. In that case there are many factors which would stop high-level casters from solving every crisis on their own, despite their power:
1) First of all, they won't be generic do-gooders. We can asssume that do-gooders will generally die before advancing to second level. High level characters are necessarily obsessed with power, and even if good, will be mostly of the smite-them-all type. Depending on the mode of NPC gaining levels, you can also have some ascetic forest-dwelling mystics/sadhus, revival evangelists or savants/researchers. Note that most of them won't have much interest in mass combat, goblin hunts etc.
2) D&D-land, despite some surface similarities, is very different from Middle Ages, and goblins are not knights in shining armor. It is, in the end, a modern game, and necessitates modern - or Dark Age- tactics. A goblin invasion will look mostly like the present "war" in Afghanistan - a swarm of small groups attacking from ambush and in the night, with the leadership sitting in some cave under magical protection from scrying.
3) As I wrote earlier, any D&D style game requires a lot of tiers of power, and they all must be filled. High-level wizards are still near the bottom end - above them are hero-deities, demigods, lesser gods, gods, greater gods, overgods etc. Moreover, most NPC casters are remarkably long-living. Taking into account the deadliness of D&D combat, it means that they spend most of their time hiding and protecting themselves from their equal-level and higher-level opponents. They prefer to act through proxies, henchmen, minions, and random idealists who can be tricked into doing their work for them - through PCs, in other words.
Do you think any high-level caster will risk burning through all his top-level spells to kill some goblins, announcing at the same time his presence to all and sundry and remaining defenceless to the counterattack of the enemy spellcasters?
4) The material world in D&D is a rather dreary and boring Third World hell-hole. Most high-level characters will find an excuse to leave it in one way or another for the planes, where they can find pleasant surroundings, real wealth and worthy opponents - in short, both interesting living and a way to increase their own power. They will tend to return to the material world only in the most dire circumstances.
5) As regard people insulting kings with impunity, one thing is certain - any king who would allow himself to be insulted with impunity, would not remain a king for long. Therefore we can safely assume that any king worthy of that name will be either high-level or will be supported by high-level people in his court.
Moreover, any long-lasting kingdom must be supported by higher tiers of power (divine at least). Any gratuitous insult to a king by high-level people will be countered by his patrons. On the other hand, a serious and justified attack likely will not be so opposed - because such an attack will have a corresponding support on the other side. But no one is going to support PCs when they engage in useless and gratuitous insults.
6). Finally, there is one reasons which will stop higher powers from doing work of PCs for them. It has been written explicitly in the Mystara books about the Immortals - they mostly allow people to manage on their own, because it is the only way for them to gain power and advance to higher levels. If the immortals did all the work for people, there would be no new Immortals.
Incidentally, I would suggest you read Lensman series by "Doc" Smith. Those books are surprising well written, and very intelligent. They are also the only literary example of the heroes growning exponentially in power in a world in which all tiers of power are already filled - which is exactly the situation that D&D PCs find themselves in. There are even over-god characters, Arisians, all-powerful and all-knowing, and their evil counterparts. Both sides, despite their power, allow humans to act for themselves, intervening only inconspicuously from time to time. Good side because they want to allow lower races to develop by themselves, and evil side, because they prefer to remain hidden and not begin the confrontation with the Good side in a compromised position.
The "Queen of the Spiders" series of adventures bears an unmistakable similarity to that series, with a hierarchy of evil races, each of which is manipulated by higher one, and no-one knowing their ultimate masters - hill giants, stone giants, fire giants, drow and unholy demon-gods.
http://en.wikipedia.org/wiki/Lensman_series
http://www.wheels.org/lens/triplanetary.html
7) Finally, since the higher-level characters are so much more powerful than low-level ones, it would be obviously inefficient for them to do things which can be done by lower level characters. Their own tasks are obviously infinitely more important. And it so happens that D&D adventures are always things which CAN be done by PCs. In fact, mere verisimilitude would require some hidden Good Side HQ which works to ensure that every new promising recruit gets to do only such things which he can do.
The only other possibility for an explanation would be the law of large numbers - there are uncounted other groups working at exactly the same task, and PCs "accidentally" happen to be the one which wins. But this becomes obviously false as soon as we get to higher levels, because it is obvious that PCs are the ONLY group trying to solve crisis after crisis - and they are strangely always succeeding.
And an aside to Elennesar: It seems to me that you dislike the level system as such. This is all right, of course. Such a system is inherently unrealistic; our Earth is certainly not level-based. But there are uncountable other levelless RPG systems. Wouldn't you consider playing eg Runequest?