But it does? It's generic, meaning you the reader are fully interchangeable with other possible subjects. At least that's the connotation it carries for me, and for what it's worth I'm a native speaker. If the reader (ie the target audience from the author's perspective) isn't interchangeable then I'd expect some other article to be used (ex they, the relevant professional, an interested party, etc).
I'm not sure it ever meant you the reader specifically, always have seen it meant to be generic or some hypothetical "one".
I'm not exactly disagreeing with that statement though. I'm claiming that it additionally carries the implication of the reader being a member of that set while alternative turns of phrase don't.
Where it gets tricky is that the reader might not be part of the audience intended by the writer.