Plato's _Phaedrus_ features Socrates arguing against writing; "They will cease to exercise memory because they rely on that which is written, calling things to remembrance no longer from within themselves, but by means of external marks." I have heard people argue that the use of calculators (and later, specifically graphing calculators) would make people worse at math; quick searching found papers like https://files…
The bit of the dialogue you quote is Plato telling a story.
On another bit he says directly: anyone can plainly see there is nothing detrimental about writing itself.
And further down the line he warns against relying on text solely to learn and not other learned people because you might lose context and internalize the wrong interpretation.
Much like you did.