The merits and flaws of Race as Class have been debated elsewhere. The focus of the discussion is wrong.
This is no-one's fault: From the outset of our hobby, every PC and every NPC was depicted through the same lens. So it should come as no surprise that, 20 years later, every bartender is a retired fighter with the HP of a dragon, every village elder is secretly a powerful wizard, and every PC need a special hook to stand apart / above the crowd.
This is a consequence of our wargaming history. Our first PCs were Heroes advanced from Fighting Men. But per Appendix N, we should be looking at Character as Class.
Conan is not simply a level 6 Warrior. He's The Warrior. When he enters the tavern, people notice. When he fights, people die. There are other mercenaries, reavers and barbarians in the world, and many of these NPCs might threaten him in a fight, but there's only one Conan. Translated to the tabletop, only PCs have the capacity to become a Warrior. One hundred NPCs might train their entire lives, but no matter how deadly they become, they will never have the suite of abilities of the Warrior. It's not a job title, it's a destiny.
Other classes should be no different. PC Clerics aren't simply priests; they are holy men with the ability to work miracles. Fantasy Popes shouldn't be able to cast spells or heal, but the party Cleric can. You are the sole living instrument of a god. Followers flock wherever you wander, lords tremble in your presence, kings have you assassinated. You're not playing Friar Tuck, you're playing Jesus.
As a Wizard, you aren't the village elder. You're Merlin. Sure, per Appendix N, evil sorcerers exist to blast your PCs with a spell (or three), but just one Wizard has traded his soul to a devil in exchange for the ability to twist reality to his whim. Even if you wanted to retired to village elder-dom, devils and demons will be beating down your tower door with contracts in hand.
And even the Thief. Whereas cutpurses work the bazars, catburglers prowl the nights, safe crackers do their magic, and assassins stew their poisons, you alone have mastery of each discipline. There is no treasure that can't be stolen, no secret that can't be revealed, no regent safe from your blade.
Extrapolated to world design it becomes clear that PCs are an explicit threat to the social order. An avalanche of plot hooks follow, simply in response to characters being Appendix N PCs. Overlords despise you; exiled kings and queens are desperate to hire you. Like Beowulf, you are the only one capable of slaying monsters. Like Merlin, you decide who sits on the throne.
Blah, blah, blah. You get the idea. Character as Class.
