The more proper question should be should children be allowed to read any material that is not absolute Torah.
If you hold that “whosoever teaches his daughter talmud teaches her tiflus” then surely allowing even boy children books that are Bobbsey Twins type books should be banned.
***scroll biographies which are not really biographies are may be borderline reading material.
Cookbooks are probably ok. Even boys may be able to read them to understand the complexity of the kitchen in order to give them a background to problems related to Taruvos.
In conclusion, Jewish Libraries should restrict their lending material to various version of Sefer Tehillim.