Now, the term "critical hit" does turn up in the first printing of D&D, but only as language grandfathered in for a very specialized form of combat. Mike Carr's First World War aerial combat wargame Fight in the Skies (1968) had long relied on critical hit tables, and the "Battle in the Skies" aerial combat rules in the Underworld & Wilderness Adventures pamphlet (where you fight on dragons or griffins, rather than biplanes) openly appropriate from Carr, down to borrowing his critical hits.
As exemplified above in Switzer's rules from APA-L #522, the earliest fan-designed critical hit systems tried to adapt this hit location concept to ordinary fighting. They also often incorporated an idea of critical "trips" or "fumbles" for exceptionally poor performance in combat (in Switzer, a trip might result in a dropped weapon, giving an enemy a free strike). Similarly, the "Warlock" system derived from the Cal Tech D&D variant, as published in the Spartan Simulation Gaming Journal #9 in August 1975, has separate tables for 2-12 critical "hit" and "fumble" outcomes, with a critical hit on the spine having a 20% chance of an instant fatality. And while Switzer has us roll a separate die to determine whether or not a critical hit or fumble occurred, "Warlock" builds the chance of a critical into the "to hit" roll itself: "Warlock" rolls percentile dice to hit rather than a d20, and one aims to roll below a target percentile, so in this chart we see the chances of a hit (CH) or fumble are scaled against the target percentage number (#) such that, if you must roll a 59 or below to hit, you will score a critical on a 3 or lower, but fumble if you roll 98 or above.
The burdensome complexity of these hit location systems must have been a barrier to adoption. None of these systems involve rolling high on a d20 roll or any of the simple damage multipliers that we associate with later critical hit systems. Indeed, nothing in the original D&D rules awarded any special privilege to rolling a natural 20: on the early attack matrices, no roll higher than 17 is ever required to hit any foe. The idea of specially privileging a roll of 20 appeared very soon after D&D, however. It can be found in the summer of 1974, in the pre-publication draft of M.A.R. Barker's Empire of the Petal Throne, as an elegant and succinct statement that an attacker scores double damage when a twenty is rolled:
A few months prior to the TSR release of Empire of the Petal Throne, the Greyhawk pamphlet applied this same idea to the system of certain magic swords. Most famously, the original "Vorpal Blade" specified in Greyhawk "will always sever the neck" on a roll of 18 through 20. Many of the other swords specified have similar mechanics: the "Sword of Cold" for one "scores triple damage when a 20 is rolled." Nowhere does Greyhawk link this to the concept of critical hits, but that didn't stop the rest of the world from making the connection. In the Samurai character class rules proposed in the Dragon #3 (1976), for example, Mike Childers gives a system for katanas complete with a "chance of critical hit" table that provides for "automatic" criticals on a "to hit" roll of 20, or in some cases lower. But this sword-based usage of "critical hits" did not become canon for D&D.
As competing game systems emerged, they almost unanimously included critical hits inspired by fan efforts to specify hit location. Bunnies & Burrows (1976) lets your rabbit score a critical on a "to hit" roll of a natural 0 on a d10, and then roll again to determine where the critical landed. The Arduin Grimoire (1977) has percentile-based tables for the results of critical hits and fumbles, though it only obliquely hints at when they should be invoked. Direct competitors like Chivalry & Sorcery (1977) and Runequest (1978) featured critical hits prominently. By this point, D&D did not merely ignore critical hit variants: it explicitly rejected them. Gygax wrote in Dragon #16 (July 1978) that "the 'critical hit' or 'double damage' on a 'to hit' die roll of 20 is particularly offensive to the precepts of D&D." When critical hits (or fumbles) are played, as he puts it, "the whole game system is perverted, and the game possibly ruined" by the precipitous deaths of powerful monsters or player characters. This text anticipates the blanket dismissal that would show up in the Dungeon Masters Guide the following year of "such rules as double damage and critical hits" (pg.61).
Nonetheless, the term "natural 20" did creep into the vocabulary of the Dungeon Masters Guide, and while many magic sword rules from Greyhawk had been modified, we still see that a weapon like the "Sword +2, Nine Lives Stealer" will draw life force from an opponent on "a natural 20." The mythical resonance of the natural 20 is too compelling to resist. Despite decades of continuing prohibition of critical hits, they were almost ubiquitously incorporated into house rules and thus the everyday play of D&D. Controlling the rulebooks does not enable you to stop a popular idea. At some point, the rulebooks have to change to meet the demands of players, and, decades too late, they did for critical hits.