Why not?Exactly and as Hank says this responsibility isn't just a case of watching over their shoulder, requesting that they don't have access to inappropriate material in areas that should be considered free from such also falls under that remit.
The child's section in a library isn't the internet, parents shouldn't be expected to have to be on their guard in such areas in the same way as they would if their child was on the internet.
Most parents bring their kids to the library and are aware of the book they are checking out. If you are as paranoid as Dan seems to be about his children's reading material then the onus is on him to monitor their library usage.