Even though this is an argument that no one's going to win, despite the fact that one could argue the same fact about Mordenkainen et al. in Greyhawk or certain novel-invented heroes in Dragonlance, here's two more cents:
1) Big time NPC's can always be elsewhere when the dung hits the ground. Considering all the extra-planar threats to the Realms (and extraterrestrial if you throw in Spelljamming), there are many enemies beyond Faerun that only high-level characters are aware off and can deal with. Likewise, many of these characters travel widely, both in-world and off, for business, research, pleasure, etc. Assuming they don't carry magic communicators, they aren't always aware of threats to their homes, or may be too far away to make a difference. If they all stayed home because something might happen, they wouldn't be the rich and successful characters that they are.
2) Many of the major NPC's do more than just fight battles. Many are involved in business, governance, family, or research of a sort. Consequently, they aren't going to deal with every little problem that crops up, and for every dragon attack, there are 10 or 12 issues of mundane theft, kidnapping, murder, and treasure hunting that PC's are more than willing to take up. This would be very appropriate in an urban setting. As for wilderness settings, PC's will often be the only ones around- no big time NPC's to bump into.
3) So what if big time NPC's are involved? In most great calamities, there are roles for everyone. The PC's may not be the biggest characters around, but that doesn't mean they don't have a part to play. Or maybe they take on the role of the unsung heroes who work for the common folk rather than the moneyed powers protected by magic and high-level NPC's. Or maybe they're tired of being unsung- rather than take this as a player feeling, use it as a character feeling and go from there. Feelings of inferiority often lead parties to do truly brave -or stupid- things, and the ones who succeed become great (the one's who don't become fodder for Elminster quotes). Or finally, try this- the NPC's show up, but the PC's get there first and deal with the problem (dumb luck, right place/right time: the ways are various and sundry). It can happen, and it makes the PC's shine in front of both the commoners and the big wigs, the latter of whom have long memories and deep pockets.
I have played in many fun FR games that don't involve biggie NPC's. When used, they were used sparingly and in character, usually as an impetus for adventure rather than a deus aut dea ex machina. Other's mileage may vary, but better to ask why and fix those issues rather than wipe the world clean.