Looks like you already know the correct sentence, but you ask "why". Some languages need an article, some do not.
I don't know the historical reason, but I can explain like this: if you say just "reader" (apart from sounding wrong), then I would be thinking "which reader? a reader I know about? all readers?" To me, the idea is not complete.
Hence it needs "the" (a specific reader), or "a" (any reader) or plural "readers' books are..." (many readers or all readers in general)
Interestingly, some flavours of English DO say "reader's book..." (without an article) e.g. Indian English. This one reason why Indian English sounds "wrong" to British English speakers. (Although this is perhaps rude, Indian English is just a different dialect and therefore not wrong!) This difference might be due to influences from Hindi or other Indian languages.