Hmm, L&S - well, if the library is in the town 5 miles away, and you don't drive, have 3 children under the age of 5 and there is a bus in each direction at maximum twice a day (though it turns straight round so you either have 5 minutes or 4 hours in town between buses), how accessible is the library physically?
And if you have a chaotic lifestyle, or have literacy problems yourself, then registering at the library (requiring, as it does, documents as proof of address and the filling in of a form), how accessible is the library practically?
And if you don't value reading or education, how accessible is the library psychologically?
I appreciate that you are talking about your own social circle and wider acquintance, and I am talking about a particular subset of parents who I have encountered as a teacher, but I find your glib comments about 'most parents' really quite irritating.
Yes, most literate parents, who have jobs that allow time to visit the library during its opening hours (the latter of course are being reduced in many places) and transport that makes the library physically accessible to them, with money for that transport and some belief that 'reading is good' can get to the library.
That does not mean that there is a substantial minority - perhaps those whose children are most in need of access to books - who have actual or psychological barriers to library access that will make it a very rare event if it is possible at all.