Many password managers use a “save new” or “update” login credentials feature that watches for newly used passwords and asks if you’d like to save the credentials used.
That’s going to go away if you remove the read access. That said, maybe that’s not such a bad thing. Plenty of people will dislike losing that feature, however.
I’m actually game for that idea, it would also make the browser responsible for parsing the many formats of html people use for structuring their input fields.