I work on books where a lot of designers are on the copyright page. And I've read a lot of books where the designer is on the copyright page. I think it may depend upon the publisher. The big ones (i.e., S&S, Random House, HarperCollins, etc. usually have the designer listed).
What gets me sometimes is that when the designer does a lousy job and I've got to carry the ball, it's his/her name on the copyright, when it should be mine. I work for a typsetting company and I've gotten some stuff from designers that leave me shaking my head. I sometimes end up doing what they should have done but were too lazy to do. (I.e., a 500 manuscript book comes in and only 1/3rd of the thing was designed–I'm told by the designer to “make it look nice” or to “feel what I am doing.”
As an aside–those pages in the back about what font is used is usually done because of trying to get to even forms for print and to keep blanks at the end to a minimum.
No offense meant to designers. Most of them do a great job. But some out there give designers a bad name. And some don't deserve credit for anything.
{EDIT: The designer is not usually the one who has overall responsibily for the final presentation. Usually it's first pass and that's it. But I”m talking about book publishing and my experience with that.
And it does depend upon the book and what kind of book. Some designer do see it through to to the end, and some don't.
I suppose I have mixed feelings about designers because of the various jobs and the how the various designers do things}