Yes, I assume the standard rules-as-written ability score generation, because I am reading directly from the rules (as written). I could argue each of the tangential rules and variants and all that jazz, but I am criticizing the RAW system, so I am quoting the RAW system. As to the second part, if your rules need a stipulation that something is "usually essential", that's poor design (and not just for the blatant oxymoron of "usually essential"). Give the stats a baseline minimum if there is one required for play. Category: I'd consider this "Broken"
Actually, some sort of sub-clause where if you have zero exceptional ability scores you are assigned one would prevent these types of rerolls, so you could argue the system could use fine-tuning if it is truly essential, but even then you cannot state this is a broken system, for the simple reason that even under this RAW system there is nothing preventing you from running a character with less then ideal ability scores, it merely indicates the general survivability. This is, however, a peripheral point, since your initial gripe was that you cannot play all classes always. Or is your argument that because the character generation system does not 100% generate a suitable character it is fundamentally broken?
Forgive me for assuming that the players might like to play the game. The adherence to Fantasy-realism goes off table the second you read the word "Dragons" in "Dungeons & Dragons". So flying lizards that breathe fire and transform their shape is fine, but a whole group of paladins working together is not? The fact that a holy warrior is super rare, yet clerics who are granted miraculous powers by an actual, provably-extant deity are a normal everyday thing is nonsensical, and doesn't really serve as evidence of a strict adherence to fantasy-realism. I get that many classes are derived from Appendix N works (Rangers from LOTR and whatnot), but their origin was phased out in later iterations... why? Because they are irrelevant. We aren't playing Lord of the Rings simulator. We aren't playing Three Hearts Three Lions simulator. We are playing D&D; a standalone, self-contained game. The fact that every later edition migrated away from these concepts is evidence that the old vestigial Appendix N stuff should not have been feeding directly into the rules, but rather just inspiring plot ideas and themes.
Category: Archaic.
You have broken up your initial point into three points, one of them improperly categorized, one irrelevant, the other invalid. You are committing an age old fallacy, that because there is fantasy therefore all semblance of realism must be thrown out the door and any sort of restriction on the frequency of exceptional heroes must also be done away with and anything goes. This point only works if you assume that there is no such thing as an immersive component to roleplaying games that could be served by having such mechanisms, that there are no degrees of realism, and that anything goes and therefore this system can have no justifiable basis. Since there are clearly people that get immersed in their characters, and some people clearly crave some baseline of versimilitude, this argument is faulty and you are wrong.
You then follow up by stating that because other editions migrated away from appendix N by taking in other influences that this is somehow beneficial but you have not demonstrated that this is the case at all. 4e was the farthest from the roots of Dnd and it clearly split the hobby in half, thus the nature of the game cannot be arbitrarily shifted. You then compound this error in logic with a second erroneous statement, that DnD is a self-contained game. You could not be more wrong. DnD is immediately recognizable and playable where other, more self-contained games are not BECAUSE so many of its concepts are borrowed from the collective fantasy consciousness. Do you think it came up with medusas, elves, dwarves, dragons, paladins? Why do you think people recognize those things without having read the monstrous manual? In fact, you will find there is an Appendix N, largely unchanged, in 5e asswell so the creators clearly thought it important. Its just that 5e players are functionally illiterate.
EDIT: In fact, one could argue, based on the recent shift TOWARDS a more prominent Appendix 'E' versus nary a headnod to its source material from 4e that the evolution is TOWARDS a firm fantasy foundation, not away from it.
Ignoring the jab at my intellect (thanks, by the way!), if you want to argue exceptional strength scores are that way to capture disproportionate stats, then why only Strength? What about the otherworldly creatures with such immense force of personality that they have CHA scores of 18/XX? What about creatures so swift that to them the world looks to be in slow motion - where is their DEX 18/XX? The line is totally arbitrary, that's why they nixed it as soon as a newer edition came along. It wasn't added to "capture disproportion" - it was added because some guy after the fact said "gee, so the super strong monster is already at Strength 18, but what if some bigger, stronger monster came along?". As for a realistic bell-curve distribution: fair point, but still not user friendly.
Category: Archaic, probably also broken by virtue of creating a STR bias where one does not exist in other stats.
First of all, your statement r.e. nixing it is inaccurate, they kept exceptional strength for 2e and only revised it with 3e, keeping it for almost 2 decades. If I were to hazard a guess I would say that strength was given an extra dimension to give more depth and playability to the fighter, and while there have been attempts to broaden all ability scores (with Dark Sun I think, though they just used an expanded decimal system) my guess would be that the practice was not adopted because it did not add overmuch. Your statement r.e. str bias is simply wrong, Dex has been the best statt for decades (and still is). You can decry that there is no such mechanism for other statts but I would argue why it is needed for other statts?
So, someone can gesture their hands to make another person explode with magic energy, yet adherence to females being weaker is where we draw a realism line. I want to know why - the only reason I can come up with is sexism, but any other explanation would be appreciated.
Category: Archaic.
This is because you judge easily and do not question your conclusions, assuming all others are foolish for not having reached the same. If everyone was born as a 300 foot tall helium-breathing spider baby before morphing into a human at their 19th birthday and then every villager in every village would have the exact same statts (18 in everything), what would your response be? What if daggers did d100 and two-handed swords did 1d2? This is a tired point, easily refuted.
Oh I saw the pattern {etc. etc}
Sorry for snipping your point old son, but you aren't saying anything new. Tables are no longer used, says you, this is the future. They said that with 4e, and they rolled back a lot of 4e. It's a fallacious argument, and as I already pointed out it can be boiled down to your preference for simpler, more intuitive systems. This is fine (I like simple systems too), but until you can address my point that this is a matter of preference, not an indication that one is broken whereas the other is hale, you aren't proving much.
Category: Broken. The rulebook is the nexus of the game - if it can't be navigated properly, that will ripple into play, manifesting as lost time, missed rulings, and a needlessly steep learning curve. While my initial point may have been about one specific rule listed, consider it an indictment of the entire system based on sloppy core technical writing.
No you are shifting your goalposts. Your point was about the rules and system as written, not the technical writing. No one is going to argue that PHB could use an edit. If you want to have a discussion about that you won't get it from me. It is also not Broken because if pointed out there are no barriers to implementation.
Part I.