I definitely don't have the historical background to answer for the entirety of human history, but I think any historian would be hard-pressed to name a time in which a communications advancement hasn't been greeted with opposition, censorship, or at best skepticism. The opposition is typically justified on the rationale that it (whether it's literacy, the printing press, the telegraph, radio, etc.) will ruin peoples' ability to think or relate to each other, or allow corrupted forms of knowledge to spread.

These criticisms were often correct in that new forms of communication and learning often change how people learn, and are actually more efficient conveyors of falsehoods than ordinary conversation. (We're all up in arms about "fake news" at the moment, but the issue is a very old one.) I think there's a strong argument to be made that most of the hysteria is just that. However, that's a discussion for someone more specialized on the subject to make, and we should also be careful before settling into the notion that everybody hated writing, or the translation of the Bible into more accessible languages, or the printing press, or whatever. Certainly pushback existed, but that doesn't mean it was universal.

Your memory is accurate. I can't say for certain whether this is the oldest recorded warning on the issue of literacy, but in Plato's Phaedrus, which was probably written around 370 BCE, Socrates comes off as a bit grumpy on the subject. He's sitting under a tree with the titular person having a discussion about love, friendship, and rhetoric, and he tells Phaedrus a story from Egypt that cautions us to revere the oral tradition of learning above the written. As an FYI, this is from the Project Gutenberg version of Phaedrus, which you can find here. And yes, we should all be aware of the vast irony of being able to link a 2,300+ year old text with a few keystrokes while discussing opposition to technological advancement in communication:

At the Egyptian city of Naucratis, there was a famous old god, whose name was Theuth (ed: Better known as Thoth in English); the bird which is called the Ibis is sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters. Now in those days the god Thamus was the king of the whole country of Egypt; and he dwelt in that great city of Upper Egypt which the Hellenes call Egyptian Thebes, and the god himself is called by them Ammon. To him came Theuth and showed his inventions, desiring that the other Egyptians might be allowed to have the benefit of them; he enumerated them, and Thamus enquired about their several uses, and praised some of them and censured others, as he approved or disapproved of them. It would take a long time to repeat all that Thamus said to Theuth in praise or blame of the various arts. But when they came to letters, This, said Theuth, will make the Egyptians wiser and give them better memories; it is a specific both for the memory and for the wit. Thamus replied: O most ingenious Theuth, the parent or inventor of an art is not always the best judge of the utility or inutility of his own inventions to the users of them. And in this instance, you who are the father of letters, from a paternal love of your own children have been led to attribute to them a quality which they cannot have; for this discovery of yours will create forgetfulness in the learners' souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves.

Thamus is kind of a jerk. A god invents writing for you and your response is effectively, "It'll make people lazy and I don't like it."

Now, here's the thing: In context, Socrates wasn't really saying that writing was horrible and that we should depend solely on the oral transmission of knowledge. Phaedrus starts out with Socrates' attempt to get Phaedrus to deliver a speech that the rhetorician Lysias has made; Phaedrus actually has a copy of the speech with him, and of course you can't exactly reproduce what someone has said without a transcription.

So what Socrates goes on to say later is that the oral transmission of knowledge has a few advantages that the written word lacks, and he's admittedly kinda right. A book can't have a conversation with you, answer your questions, or directly correct you if you've misjudged something in the text. You can read a book, remember what it says, and parrot the knowledge you've gained with the appearance of being a learned person. (In English, we call this "college.") However, you won't have had the benefit of intellectual give-and-take that Socrates prized so highly in the oral tradition of learning, and that eventually became known as the Socratic Method for just this reason.

You can argue that Socrates had the last laugh, because he never wrote anything down and is yet still revered as one of the greatest teachers of all time, with his methods still employed (with varying degrees of success) in universities around the world. The Oxford/Cambridge tutorial and the law school seminar are direct descendants of how Socrates and his contemporaries taught students. However, you can also argue that the people who paid no attention to Socrates' bitching about writing had the last laugh, because the only reason we know about him at all is because ... well, people wrote down what he said, copies went everywhere, got translated, and are still with us today.

So, from the perspective of the 21st century, it's madness to argue that literacy hasn't been a bedrock of human advancement. Books have their faults, but the written word functions to store and reproduce knowledge at a rate that no one teacher, however gifted, could ever hope to do. Ideally you try to combine the two, and in the end, you wind up with something that looks an awful lot like how we teach students today: A combination of books (the written word) and teachers (the oral tradition).

What really fascinates me about this whole discussion is how closely it mirrors fairly recent arguments about Google and its impact on how we learn and remember things (Do we remember things we learn from Google, or are we more likely to remember how to find them again? And does it matter?), and equally recent arguments about distance learning and what we sacrifice by not having students physically in a classroom with a teacher.