Phone books do seem to be coming in increasing numbers because companies make money on ads they sell in those books.
The only phone book required by the Kentucky Public Service Commission is the one from your official phone carrier, in Lexington that's Windstream.
They must print a paper directory once a year, it's usually around April or May.
The PSC did allow one company, Cincinnati Bell, to distribute its northern Kentucky white pages only online, so far it's the only company to do that. As for all the other books, there's no regulation on who can or can't give you a book. As for what to do with them all, you can put them in your recycling.