This thread generates a lot of interesting observations, keep it up.
I've decided to put my money where my mouth is - I've dusted off the old AD&D PHB to pull some specific examples of the game being broken and/or antiquated. Let's start from the top!
Might I have...this dance?
I daresay most of these points are trivial to address but I would be skipping a much more important point that must be made first. It should be easy for you to outline your preference for 5e over 1e in a short list of comprehensive bullet points so we can understand what your parameters are before we wade into a laundry list of specific rules that you (for us) arbitrarily dislike. In short; if you cannot tell us why you like one game over another in short and succinct fashion the argument is going to get mired in an endless and ever-shifting morass of nebulous positions.
With the current list of specific points your argument against 1e is easier to address because you have outlined your accusation more specifically. These rules are either 'broken' (i.e. detrimental to game-balance or disruptive of the game as it is meant to be played) or 'antiquated' (superceded by more accurate, more efficient systems).
Rolled mediocre attributes? Cool, half the classes can't be played by you now! No paladins, monks, rangers, assassins, illusionists, druids... half the game content locked behind a random dice roll!
You assume standard ability score generation, not one of the half-dozen alternate methods of ability score generation but that is acceptable. You also ignore 1e's adminition that it is 'usually essential to the character's survival to be exceptional (with a rating of 15 or above)' (PHB p.9) so this mediocre scenario is much less likely then you make it out to be.
The whole point of these classes is that they are meant to be fairly rare, professions for exceptional men, and the ability requirement rules enforce this rarity so the GM doesn't have to step in when the party is composed entirely of paladins and gnome illusionist, much less when the GM conceives of a nation where all fighting men are paladins. They are meant to enforce a sort of fantasy realism for both player and GM. The very idea of the paladin is one of exceptionalism, and with good reason. A holy warrior imbued with supernatural gifts by the forces of good should be much rarer then a fighting man under the assumptions the fantasy system is based on. Contrast this with 5e, where no rules-based argument may be formulated for the frequency of Fighters over Paladins, Barbarians over Monks etc. etc.
Strength seems pretty straight forward as a concept, right? Nope! Heavy door? Open Door on X roll when Strength is Y . Oh, but it's a "gate" not a "door"? Better look at the "Lift Gates" percentage instead. Yeah, all those situation-specific skill caveats are never going to get annoying. Don't even get me started on Strength scores higher than 18 - that 18/XX shit is totally not vestigial and useless (/sarcasm).
It is curious, in your line of argumentation, everything, even seemingly complex things, seem so very straightforward or otherwise entirely arbitrary. Perhaps it is because of your dizzying intellect, piercing through mists of obfuscation? In general I will wholly admit a straightforward d20 + ability score mod versus a DC is more intuitive, and is also the reason I prefer Basic DnD. In defence of AD&D; These percentages are so wildly different because the chance of success should realistically be wildly disproportionate depending on one's strength score, and the increase in success chance is not a linear +5% with each two points of Strength as in 5e, but follows a more realistic bell curve distribution (i.e. the same door is not 25% more likely to be broken open by a man with 20 str then a man with 10 str). The exceptional strength, while certainly unwieldy compared to the simple model of 5e and basic, is designed along similar lines. The idea of the system is to simulate, for fighters, characters of exceptional strength at the edge of the bell-curve without relegating them to the domain of superhuman ability (hill giant strength).
Hey, gender-based stat restrictions - Female characters have a maximum Strength score! Yeah, sexism isn't an antiquated part of the game at all...
First of all, in order for it to be sexist it has to be based on prejudice, not reality, no matter what your college professors tell you. Female upper body strength is statistically much lower. Since most adventurers were considered exceptional individuals anyway, this rule was later dropped, probably with good reason. I'll fully agree its antiquated because it doesn't reflect actual play
Thief skills. You know what's cool? Not having completely arbitrary percentages to do different thief actions. Why does a DEX 17 thief have a +10% chance to open locks but a +0% chance of locating/removing traps? Because of reasons!
Again, just because you cannot find a pattern does not mean no such logic exists. Clearly removing traps is considered a more complex task and therefore only 18 dex gives +5%, while it also gives a +10% to lock picking. Are you starting to see a pattern? Can you infer what bonus 19 dex would give? It is almost as if there were some sort of...distribution, some sort of...curve? that is being modelled for some reason. You can say its less streamlined or harder to use but it is more realistic. That's the central tradeoff that is being considered.
Here's a fun little line tucked well away on page 10: "Change in intelligence: If Intelligence goes up or down for any reason and such change is relatively permanent, the magic-user must check again as explained above for know spells by level group". Better hope you remembered a throwaway line at character creation, otherwise you're cheating whenever your INT changes.
Argument against the layout, not the substance. You can argue that 1e is poorly laid out, I think few will disagree with you.
Races and classes don't mix! Dwarf magic user? Nope! Can't exist! The only monks are Human, because that makes sense... those deeply spiritual elves would never become monks! Halfling assassin? Nope, no tiny ninja hiding in a giant cake to jump out and murder the corrupted Duke at his 60th birthday party allowed! Halflings can be fighters, and halflings can be thieves, but a halfling thief that can also fight people? NEVER! Don't you just love arbitrary restriction in your free-form sandbox games? Nothing is more fun than hamstringing player options!
Where do you think halflings and dwarves come from DP? Have you heard of something called an Archetype? Do you think a race of stone age bird people living on mountain crags and worshipping the spirits of their ancestors should have the equivalent of a christian crusader class? Your demand for no restrictions actually makes the game much more arbitrary and races and classes less meaningful.
Even more caveats! There's a whole table of level limitations based on class and race. Did you know Elf fighters with less than 17 STR are limited to 5th level? Nothing like halting character progression dead because of a single low dice roll you made twenty sessions ago way back at the start of the game.
Again, restrictions meant to simulate a certain fantasy milieu and its underlying assumptions. One might argue it explains why all the greatest practitioners in the world are not held by longer-lived demi-humans. You also omit the possibility of multi-classing for demi-humans, which increases this longevity well into the higher reaches of a DnD campaign. A molehill is turned into a mountain range.
Here's a legit line from the PHB: "However this nature gives them a bonus with regard to their saving throws against attacks made by magic wands, staves, rods and spells. This bonus is +1 for every 3 1/2 points of Constitution ability"... yeah, that's way more straightforward than "Advantage on saves against magic". Also wands/staves/rods having its own category of saving throw is really dumb.
Do you understand there is always a trade-off between usability and complexity/realism? All your argumentation is based on simplicity and ease of use, which is fine, but then you don't get to complain when people write you off as a filthy casual or call your edition a baby's edition right? Why is a separate category for magical devices versus the personalized spellcasting done by spellcasters a problem? You can use different saving throw progressions to fine-tune the effectiveness of some classes versus enemy spellcasters in this fashion. Under the current ruleset the resistance is explicitly tied to a Dwarf's natural hardiness, under Advantage this is A) not the case and B) is much more powerful.
Shit I'm only on page 15 of the PHB... this is too much. I'd go on, but then I'd become like squeen and his infamous walls-of-text ("gaze not into the abyss", and so on). I think I've belabored my point enough, but I've got my trusty copy at hand if anyone wants more.
If this feels tiresome it is only because the counter-argument has been repeated to you so often one would think it is imprinted on your optic nerve by now. AD&D has a much firmer idea of the type of fantasy it is trying to be (poorly articulated though it may be) and its rules reflect that at the cost of simplicity.