I keep only infants and young toddlers so I FEEL you!!
I mounted higher shelves and keep them in bins out of reach. They can see them, get excited and run to their spots on the mats when I go to get them down each morning.
When it is "Book Time" we do it in the circle on the mats as a group activity (like manipulative's). I collect them before they go back to free play.
"Reading Time" is done on their nap mats since that is followed by "Night, night my sweet".
I do have a small bin of board books in my quiet corner, though. Kids are only allowed there one at a time, with permission, and treat those books like gold.