I personally would not touch this book with a press. First of all you have you have creasing and broken color top and bottom corners and along the top edge. A press many tone those down a bit, but its not going to remove them. The rear cover shot, the spine looks a bit weak with wear and tear along it, and maybe the staples. Heat from a press is not going to help that.
Pressing to me is more for getting rid of spine rolled books, cover warping and wrinkling, and bends, or stacking curl, but its your choice of course. You can press that book from now to doomsday but the creases and color breaks are still going to be there, just a bit less notice able.
Just my