The title page of a chapter need not have them either, but most other pages of a book should give the reader some guidance as to where they are in the book they are reading.
This applies to anything I create, as well as the design of running headers and footers. I always take a fresh look at my design, and take away what is not necessary. Like many book designers, I have a tendency to over design. The title page and copyright page, for instance, need not have them at all. There are particular pages where it is accepted practice not to place running headers and footers. They can contain the title of the book, page numbers, a part of a book, a chapter, a section, or any other reference point. The running head is at the top of the page and the running foot is at the bottom. Running headers and footers are displayed at the top and bottom of pages. Running headers and footers are parts of a book.