I work at a print shop. We print books all of the time, and sometimes on plastic, also known as synthetic papers. Most modern synthetic papers don't require special inks or procedures. We use the same soy based inks in the same machines with very few minor changes in the process. Here's a link to a brand we frequently use:
http://www.polyart.com/en/synthetic-paper/extraordinary-synthetic-paper/how-it-prints
The real reason we don't print most of our books on plastic is because most people don't want their books printed on plastic. Books have a very long history, and often times in this digital age, the whole point of having a book printed is to give it a link to tradition. People still like reading books, and they still enjoy the tactile sensation of turning a page. Synthetic papers don't feel the same way. They're also more expensive. So for most people, it defeats the purpose of having a book printed and is more costly.
Though for some people, the synthetic papers make more sense. Especially if the book is going to be subjected to the elements, like a book with survival tips (though if you need to build a fire to survive, you can't use the book as kindling), weather chasing, or boat repair.