iserith
Magic Wordsmith
I think that your comment about an innate sense of fairness captures a good deal of the debate, which is often overlooked.
I'd like to address your last question. It really goes to how the table plays. There are tables that view this as a game, and the character is, for lack of a better word, the Heroic embodiment of YOU. It is you, awesomer, elvier, stronger, less jerky, etc., and winning! It is an alter ego to a certain extent, but it is also how someone imagines they would be, if they were ... you know, that character. In that way, stats, etc., are just numbers used to accomplish things (like rolling to recall lore).
Others prefer to play characters more as the characters themselves. In other words, they consider the character as a completely separate creation; an entity with its own drives, and feelings, because that aspect is interesting to them. They don't think about what they would do tactically, but what their character (with the benefits and limitations of that character) would do tactically. The ability scores help define the character in their mind; it's more than just a stat to roll against.
I present this as two binaries, but most people play somewhere between the extremes. For example, the alter ego players will create backstories, have flaws, and so on, as that's part of the game. And the "characters as characters" are necessarily limited by the fact that, well, they probably don't know what an elf really thinks, and can't possibly play all ranges from a 6 - 20 intelligence, and so on. But they are different view points.
It bleeds into other aspects of the game as well. IMO, it may also correlate with the amount of "roleplaying" (as in talking through things) vs. roll-playing (as in use the dice to determine social encounters), but that's just a guess.
As you say, most likely sit in the middle of those two approaches for the reasons stated. What is notable about the bit I bolded above is that there may be a perception that you are required to impose limitations on your decisions based on some idea of what a particular ability score represents. Failing to do so is "unfair." This goes beyond the realm of mere preferences, I think. In theory, people in the two camps you outline above should have no problem with each other at the same table. It's when there's a perception of unfairness that suddenly Bob is telling Mike how he needs to play his character because Int 8.
And if that is so, then the solution as I see it (if there is one) is to get at why it's seen as unfair and resolve it. Could it be past editions of the game, I wonder? Did past editions of the game suggest there was a way to correctly play a particular score (read: fair) and this has carried over into more modern versions of the game?