The "RAW is holy writ" thing did start in 3e, in my experience. The factors that led to it's inception are quite interesting, and I wish I had the patience to do some detailed research- it seems like the kind of information that would be important for posterity.
Simply put, as near as I can tell, it resulted from a combination of factors, the most notably being the internet and WotC forums. Previously, one player's contact with others was limited to chance encounters or going to a convention- most gaming groups in a given geographical area seemed to have very similar views of the rules and how they worked (or didn't).
DM fiat was a huge deal in the AD&D era, especially, where you had to do some deep diving to find some rules buried in the text, and even once you knew about them, you might balk at applying them.
I used to play a fun game with other AD&D players where I would bring up a rule that totally exists and have them argue with me that no such rule ever existed. Then, once I proved it to them, they would just mutter something about how "we didn't play it that way".
(My personal favorite was found in the saving throws section of the 2e PHB, where it allowed you to add your armor's magical bonus to saving throws, which I'll put here).
But suddenly, many players and DM's were on forums, talking about the new edition. When discussing the game, it was quickly realized that having a discussion where everyone is using their house rules was usually a non-starter, so it became convenient to discuss the rules as written. But even more, this is where people really started to compare notes about the (ab)uses of DM fiat in the AD&D era. Nightmare DM stories proved quite popular, and many players started to realize that their DM's would often substitute the rules of the game for their own whims, and in the hands of some DM's, this created a miserable experience.
And so players started to demand that the DM play by the rules, so that things would be "fair" (whether or not this led to actual fairness I can't say- as was eventually determined, WotC's rules could lead to some very broken situations). Players could point towards encounter design guidelines, encounters per day, xp guidelines, and wealth guidelines, as well as the fact that some kind of magic items were assumed by the game, and would pressure their DM's to not deny them things the game itself was telling them they should have.
The fact that even monsters now generally had to follow the same rules as characters was the start of a "transparency era", where players felt entitled to knowing how things in the game worked, especially given the descriptions for knowledge checks.
Some old school DMing strategies became reviled, such as low magic campaigns, denying players information about things in the game world, and the "plot railroad".
A general sense of "if the DM follows the guidelines, the game will function just fine" came about, to the point that if you, as a DM, went to an online forum looking for advice, the very first response you'd get would very likely be "are you following the wealth by level guidelines?"
When 4e was created, the developers doubled down on this transparency, making sure to tell DM's that it was better to not keep players in the dark about how things worked, as it let them make more meaningful decisions.
Now, at no point did the DM ever lose their power of fiat; in fact, every game usually had a fairly extensive list of houserules. But some DM's did, in fact, balk at the idea that a Fighter would be expected to have a +1 sword by level 2 or 3 (and that the game's math was built around this assumption). Or that players could make their own magic items. Or that players could make a DC 20 Knowledge check and know pertinent information about a monster they were fighting.
I'm not going to weigh in on which approach is better, though I have my preference. While the new approach tended to avoid "gotcha" moments, which I've never cared for as a player or DM, many DM's did, in fact, feel like they had lost control of the game. It used to be that you accepted the DM's rulings or you didn't play D&D.
Suddenly, it felt like that was inverted- that unless the DM had the players' trust, they would revolt.
