I exchanged some emails with the overdrive people, suggesting that they use more of the screen space for text, and less for other information (time of day, batter level, images to make it look like a book, current page, etc. The response:
The issue is actually with the formatting of the book and not with the
OverDrive app. The publishers specify the amount of white space to
display in their metadata with the title. Unfortunately while this
works for larger screens, it does not always render the best on smaller
screens. This will vary depending on the ebook that you have checked
out and are viewing.
OverDrive Support Team