I personally do not care about the +5. I am just pointing out the flawed logic if these attribute bonuses, are as you say, cultural. I mean, I get it. The attribute system is flawed no matter how you look at it. But let's at least supply some logic behind it. The starting attribute bonus is nature, and then as your character trains, it improves, which is nurture.
This ignores a few things.
First, and perhaps the most troubling, is that this takes the position that some people are just born more intelligent than others. And, you'll notice, that those who are born stronger and tougher (more suited for physical work) are rarely born smarter. In fact, one of the more common combos is Intelligence and Charisma, which makes for a good leader.
So, some people are born to be leaders and others are born to do manual labor, and if you are starting to hear a sound, that might be a dog whistle for some really destructive and dangerous rhetoric that a lot of us do not want in our games.
Additionally, let us not forget that DnD characters start out as adults, not babies or small children. Why is this important? Because if a guy has been lifting weights and strength training from age 10 to age 25, then I'd expect him to be incredibly strong. The culture angle would explain this, and yes, you run into weird cases with elves and dwarves and other long lived races, because logically someone who is trains from 10 to 200 would be even stronger. But this is not a problem only for this, this is a problem for all elves and dwarves for the entire game. Why do they barely have any more skills or weapons training than a human who likely has been doing it for no more than 6 years? This has always been an issue and whatever solution you've been using probably could work here too.
No. The point is about one side wants a 16 to start with. The other side doesn't. WotC decided they wanted a 16 because it is easier. The 16 crowd applauds the decision. The 15 crowd thinks it does nothing to better the game, and in fact, may hurt it in the long run.
As far as your approach, (and I am sorry) but all I have seen is dismissiveness. Giving you the examples in the PHB as against type, and you dismiss their definition and expand it to match your own. Given quotes from the DMG and PHB about traits, and you interpret it with only one lens. Having Oofta and others patiently explain how it is possible that the deconstruction of patterns can also deconstruct lore, and you eloquently, yet numerous times, say it won't.
My advice (and I know you are not asking, but I am giving it anyway) would be to approach it as if Oofta is correct. It will homogenize the races. But then point out the positive benefits it will have on lore. You started down this road with me with the nature vs nurture debate, but then I was the jerk that didn't let it go. Sorry.
If I accept the PHB defintion, then the only possible way to play against type is to have a poor stat match up. It reduces a narrative choice down to numbers. Like you said, do I have a 15 or a 16.
And, I'm sorry, but that is not what that term means in the broader context of storytelling, acting, roleplaying, ect. And additionally... how boring is that? Not to attack anyone here, purely looking at the PHB, but I could play the most stereotypical dwarf ever, and since he is a monk with a 15 Dex he is against type? And if I am playing a technology loving High Elf who hates the forest, but I have a 16 in Int... I'm playing fully into my archetype as an elf?
And, I've covered your quotes from the PHB, and pointed out that they cover the entire section. Your assertion that those quotes are meant to apply to racial ASIs is akin to going to the Bakery section at a store and saying that everything inside is made from Bread. While, yes, the bakery sells bread, they also sell many products that are not bread, and simply being in a bakery does not make something bread.
But I think my biggest problem with your suggestion here, is that you want me to assume the other side is right. And I have two issues with that.
First, if I responded by saying "Yes you are right about your assertion, but..." then their response will natural be, "That doesn't matter, because [repeat assertion]." Oofta has actually done this already. He has said that the things this rule adds to the game are overshadowed by the things it loses. So, your advice would be for me to say "Yes, this rule is a net loss for the game." and at that point, I'm just conceding my entire position.
And secondly, I am freeing the other side from the burden of proof. I don't know why I see this time and time again, but it makes no sense. If you want to convince me of something, don't tell me to go convince myself that you are right. By approaching this from the position that my opposition must be correct, then I lose all ability to counter-claim, all ability to provide opposing evidence, all ability to say that my points alter the scales to lean in my favor. And meanwhile, all the other side has to do is make a claim. They need to put in zero effort to defend that claim, zero effort to support that claim, they just get to say something and I'll tell them they are right.
Well, I'm sorry. I don't do that. I do not just assume that the person I'm arguing with is 100% correct in their assertions. At that point, there is no need to argue at all.
The real answer is because rules need to be balanced. But that won't suffice for you. I mean technically, there is lore for elves to be dexterous, wise, charismatic, and intelligent. But the PHB needs to balance the races out, so they focus on the ones that
best fit the archetype. It's like the old multiple choice questions:
1. Choose the character trait that
best defines an orc.
A) Strength
B) Dexterity
C) Wisdom
D) Charisma
You wink as though that is an obvious answer. But, this misses two points.
The first? You get more than one character trait as your ASI. Orcs got Strength and Con, but in the same book Tritons got Con, Charisma and Strength. So, I have no need to limit myself to a single answer anyways.
Secondly, Wisdom does make sense. A lot of sense. Wisdom is the stat associated with Clerical and Druidic magic. As a race that heavily favors the worship of gods, wisdom makes sense. In Eberron Orcs are the source of Druidic magic in the setting, tying into the imagery of orc shamans which is very common for the tribal people tropes that orcs play into.
Also, what is one of the big things about their relationship with the gods? Signs, omens and portents. Orcs are constantly observing the natural world, looking for signs. They are... perceptive, seeking insight into the meaning of these signs. I'm sure you are seeing what I did there. Any other skills they should be good at? Yes. Survival is a by word for the orcs, who being a tribal people would by necessity be good at tracking, hunting, gathering food, finding water. Their life style fully supports this idea. Anything else, actually, again, yeah. Animal Handling may seem strange, but Volo's did give us two examples. Red Fangs of Shargaas raise and ride Giant Bats and one of only 4 beasts the book added were Aurochs. Sacred oxen that the Orcs who revere Bahgtru raise and ride into battle.
And, to support this even further. The "Eberron" Orc is the one everyone is saying is canon now (mostly because it is the version of the Orc without the Int penalty) is also a version that gets the ability "Primal Intuition" which allows them proficiency in two of the following, Animal Handling, Insight, Intimidation, Medicine, Nature, Perception, Survival. And, if you break that list down you see 1 charisma skill, 1 Intelligence skill and 5 wisdom skills, showing a clear predominance towards wisdom.
So, sure, many people want to pigeon hole orcs into "Orc Strong" and leave it there. But, since I'm not required to be limited to one choice, and there is a lot stacked up over here in wisdom.... Why not pick wisdom?