But if the game that a group of people are playing is "Let's generate PCs, then play them through a 100-session campaign, in which the outcomes over the course of the campaign will depend heavily upon action resolution, and action resolution will in turn depend heavily upon stat modifiers", then it is not true that rolling for stats gives everyone the same material, opportunity and choices. Some get high stats, others low stats, which - relative to the game they are playing - is unequal material, unequal opportunities and unequal choices.
Let's try to break this down, because this is your first core mistake right here. "Depend heavily upon stat modifiers."
Looking at the mechanics of D&D we can see the following:
To Hit = d20+proficiency+stat mod+weapon mod vs. AC value in most cases. If you have one PC with a 15 in a stat and another who rolled a 16, all else being equal for say a 1st level PC against an AC opponent, you'd have:
d20+2+2 vs AC 15. On a 1-10 he misses, on an 11-20 is a hit
d20+2+3 vs AC 15. On a 1-9 he misses, on a 10-20 is a hit
Seems to me that the odds on hitting the target do not "depend heavily" on the stat difference, as it's just a very minor increase in the chance to hit. And that's even assuming that the person who rolls random stats will always have higher stats than the point buy or array, and that's already been demonstrated to not be true.
I'm sorry, but if you (general you) are going to rely on hyperbole (I'm being punished, it's not fair, it heavily depends on) that isn't even the proper way to use these words and phrases, I'm going to have a hard time buying into your argument.
Wanting to play a game in which PCs have equal chances of impacting the fiction, where that equality is not expressed in terms of a one-off gamble but is an equality that endures over the course of the game, in virtue of roughly comparable capabilities in respect of action resolution, is not immature. Maybe you don't like that style of play, but so what? "Wanting to play the same game as Sacrosanct" is not any sort of necessary condition of maturity.
Firstly, this isn't about playing the way I want to play. You can put that strawman to bed right now. Secondly, let's just clarify your statement because I clearly want to make sure I'm not misinterpreting. This sentence above seems to imply that a player who demands that every PC at the table has the exact same score for each of the abilities as every other PC at the table, that is not an immature behavior, and isn't fair*. After all, every PC makes every type of stat roll at some point in the game, whether it be an attack roll, a saving throw, or an ability check. You're talking about how an ability modifier "endures over the course of a game", and how every PC should have the same equality in that measurement. That means, and is dependent on, every PC having the same ability modifier (equal chance) for every one of their stats since every stat is used "over the course of the game."
Otherwise, where do you draw the line? Every PC should have the same attack roll modifier, but not saving throw modifier? Every PC should have the same attack and saving throw modifiers, but not skill checks?
Basically, in order for your argument to have any sort of weight, you have to get rid of random rolling altogether in the game, and every PC would have to have the exact same stats. That's the required criteria needed in order to meet your conditions above, since the success of a to hit roll is a lot more heavily dependent on a random d20 roll than an ability modifier, and the only way to achieve "equity over the course of the game" is to eliminate randomness and make everyone the same.
And I'm going to head off one of your counter arguments right now. I imagine a typical response you (or someone else) might have to this is, "No, not every stat should be the exact same, but the pool of stat bonuses should be, and the players can choose where to put them." yes, that's true. But the players also
choose whether to use array, point buy, or random rolls. If everyone was given the same choices, complaining about a player who chose to roll and got a higher stat as unfair is literally the same thing as complaining about a player who chose to put his +2 modifier in dexterity when you chose to put a +0 modifier there (both using the same arrays) when you both have to make a dex saving throw.
*my argument was that saying that if you think it's not fair to you because another player has a higher stat when everyone was given the same opportunity choices, is immature behavior, and you're clearly disagreeing with that