Arial Black
Adventurer
But, your presumption is that all PC's and NPC's are created using the same method. That is not necessarily true, nor is it even assumed by the game.
For human PCs (and the equivalent applies to each PC race) all PC humans are...human! However humans are generated/created, that's how ALL humans are created/generated in the game world (as opposed to the meta-game players around a table).
In D&D, from its inception, 'humans' are created/generated on 3d6 in order. It is assumed that, conceptually, all humans were created/generated this way, resulting in the human population of the world.
Every single one of these humans is a potential PC. Imagine that the players could review the character sheets of every single one of these inhabitants and then choose to play one as if it were a pre-generated PC.
That is and always was the presumption of D&D.
But Gygax realised that most people aren't going to be adventurers. So he thought of various ways to get better-than-average results for ability scores, based on the concept that most adventurers would be more gifted than non-adventurers.
He thought of 3d6 six times but arrange as desired (as opposed the the general population's in order). He thought of 3d6 twelve times, choose any (i.e. 'the best') six scores and assign them as you wish. He thought of 4d6k3, assign as you wish.
He thought of a few others too. But the crucial thing about each and every one of these 'PC generation' methods is that these humans are not a different species with different assumptions! This is just a way to choose the better humans to play. The assumption remained that, conceptually, whatever method the player actually used to generate those stats, the resulting PC is simply one of the luckier humans whose creation in world was 3d6 in order, just like everyone else.
This applies to NPCs and PCs alike. When you meet a commoner, conceptually, each of his ability scores was generated by 3d6 in order. Any of his stats could be as low as 3 and as high as 18, with no 'zero sum game' going on. Even if the DM can't be bothered to actually roll those scores, or go to the trouble of creating a full character sheet for this shopkeeper/beggar/prostitute/barman (and why should he go to all that trouble for 'window dressing'-type NPCs), conceptualy every single human has a full character sheet with six scores rolled on 3d6 in order.
The upshot is that, whatever method we actually use to generate the scores for our PCs, they will still be conceptually rolled on 3d6 in order. Therefore any combination of six scores of 3-18 are a valid PC or NPC, and any PC generation method that restricts those possibilities takes away valid concepts to play.
So 3d6 in order, 3d6 six times and arrange, 3d6 twelve times and arrange, 4d6k3 and arrange; none of these methods takes away any concept. Contrast that with 2d6+6 six times and arrange, which takes away every concept that includes a 7 or less.
What point-buy and standard array methods do is take away the vast majority of possible concepts, leaving a pitifully few when compared to 3-18 six times. If you want to play one of that huge majority of concepts you are S out of L with those methods.
Now, if you treat D&D as a board game where the priority of 'PC parity' is more important to you than realism, then these methods seem like they do that. Rolling almost certainly doesn't do that, so point-buy/array seem...'fairer' (meaning, of course, 'balanced').
It's an illusion though. The results of point-buy/array (the resulting PCs) are not really balanced, due to things like MAD versus SAD, the utility of each stat to each PC in the game, variations in system mastery, and so on.
So, for me, point-buy/array throw the baby out with the bathwater. Realism has been thrown away in favour of balance, without actually achieving that balance.