My old AD&D groups never really settled on a consistent method. I think we sometimes used Method I (4d6, drop lowest, arrange as needed) or even a variant using 5d6, but I don’t think we even knew about the other three official PHB methods or the overpowered UA Method V.
Three other
DMG methods, which I think is part of why others got overlooked, since they didn't put any method in the PH!

Method V I feel more sympathy for nowadays, given how powerful demi-humans are, especially the new ones in UA.
At the time I compared the B/X rules with the PHB and noticed that the AD&D ability score system was much stingier with bonuses and much less consistent in general. B/X and BECMI had that nice smooth bell curve seemingly designed for 3d6 rolls, easily memorized once you got used to it. The pluses and minuses were consistent across the six abilities and you could get a +1 bonus from a mere 13, so characters did not really need super high scores. In fact a B/X character with all 13’s could probably be pretty successful (can’t remember if you needed higher scores to qualify for classes).
Whereas in AD&D even a 15 barely got you anything much, and the massive advantages for the highest scores and serious drawbacks for low or even medium scores created a perverse incentive to fudge or cheat. For warrior classes percentile strength and +3 or +4 hit points for 17-18 CON were too tantalizing to give up. Spellcasters needed very high INT or WIS if they wanted to get bonus spells, learn the highest level spells, or avoid getting locked out of good lower level spells by a failed attempt to learn. Thieves really needed that high DEX boost for their mediocre chances to use their abilities. And of course you had the “win more” XP bonus for high scores in prime requisites.
I think that retaining the 1E ability score tables was one of the biggest problems with the 2E PHB, no doubt done in the name of backwards compatibility. They then compounded the error by listing 3d6 down the line as the first of several methods. The 2E PHB had a sample fighter character called Rath with a 14 STR and no other high scores, and we mocked that character and the accompanying instructional text as unrealistic given the demands of the game. If I ever decide to run an “old school” D&D game again, I would probably use 2E with B/X ability scores and Method I.
I've ranted repeatedly about basically everything you wrote there. Yup. The B/X and BECMI system and bonus distribution also made a score of 13+ more accessible thanks to the point-swap rule to increase your prime requisite.
There are no high scores required to qualify for classes in B/X. Just min Con of 9 to be a Dwarf, Int 9 or better to be an Elf, and both Con and Dex of 9 or better for a Halfling.
The pluses and minuses aren't quite identical across all six - Charisma is the odd one out, only giving a +1 for 13-17 or -1 for 4-8, and needing a 3 or 18 for a -2 or +2, because of course those bonuses are being applied to 2d6 rolls for NPC/monster reactions and for henchman loyalty and morale, so a smaller bonus is a much bigger deal than it is on a d20 attack roll or saving throw.
This is from AD&D. Use this as gospel. If they roll a character without these traits...reroll. 16 or above in at least one, just to make sure.
Using that as a qualifier means that you usually can end up with a feasible character. It may be fun to ignore it and see how well you can do, but the reason so many had higher scores at tmes (if they weren't cheating to make them) were due to following the above rule.
it's amazing how many more 17 and 18s get rolled when you have to scrap any character that doesn't have at least two ability scores that are 15 or higher.
Not always, but a higher chance of it. Normally out of a party of 5 or 6 at least one character will have an 18 and several may have a 17 in one of their ability scores.
Combine that with my fairness doctrine (everyone rolls up a character, but you can use anyone's rolls that you want, so if your friend rolled better than you, you can se the rolls they made instead...thus no one feels left out because they rolled "badly" comparatively to everyone else).
Due to the two things above, there were times where everyone in the party had one ability score that was 18 and another that was 15 or higher.
AD&D is a statistically interesting case.
The odds of rolling 15 or better on 3d6 are about 10% (19/216). In Gary's world we can infer that to get tangible bonuses from ability scores your PC should be in the 90th percentile.
A few months ago I asked myself: how many NPCs in Hommelet have at least one exceptional score?
A little futzing with combinatorics on 3d6 and the binomial formula gives the answer: about 40% have at least one 15. And about 10% of NPCs will have 2. So feel free to give that guard captain a 16 strength or the mayor a 15 charisma. You're not inconsistent with verisimilitude.
So requiring viable PCs to have 2 exceptional scores is not that high a bar. Of course, NPCs are just as likely to have penalizing low scores as high ones. The 4d6 method gives you a much higher chance of getting those two 15+ scores, while vastly mitigating the risk of a very low score.
And in my current campaign I also used the "fairness doctrine" that a player can make their PC using any other player's array.
Yeah, if a 15 or better is around 10%, and you need two of them, you're usually going to wind up rolling up a LOT of sets using 3d6.
No wonder Gary wrote in the DMG
"While it is possible to generate some fairly playable characters by rolling 3d6, there is often an extended period of attempts at finding a suitable one due to quirks of the dice*. Furthermore these rather marginal characters tend to have short life expectancy -which tends to discourage new players, as does having to make do with some character of a race and/or class which he or she really can't or won't identify with. Character generation, then, is a serious matter, and it is recommended that the following systems be used. Four alternatives are offered for player characters."
I like that fairness doctrine rule as well and I've used it once so far.
I don't like the huge numbers of re-rolls necessitated by setting two 15s or better as the required floor, even using Method I the number of re-rolls usually needed seems annoying. Employing the Fairness Doctrine seems like a pretty good help, though. Across your whole group SOMEONE should get a set which clears the bar. And if no one does, I'm sure that would be kind of a fun group experience too- "Ok, no one hit the numbers, so everyone gets to re-roll!"
When I'm running B/X or another game on that scale my usual mitigation against re-rolls and hopeless characters is just to allow "flipping" the set. Roll 3d6 down the line but then you may optionally subtract every score, in order, from 21. This means you never have to take a below-average set.
But Method I or Method III (which has an average value of about 14.2 compared to Method I's 12.2) plus Fairness Doctrine seems like it should cut down a lot on a need for re-tries in AD&D.
*(Gary, on the previous page you just showed us a bell curve; you know it's not "quirks" of the dice, right?)