To answer your question, yes, I would be interested in this product, and a lot of other people would be as well (most of whom are using the HelloBar). So is there a use case? The answer is yes.
How to improve: I would consider making options that are the size you show on the site and also larger. Something that slides down and looks beautiful and serves the purpose that a pop-up serves. I feel like this would be less intrusive than a pop-up (everyone hates them) and would allow website owners to show more info than a single line. So as you mention, an author could have a "drop-down" instead of a "pop-up" that shows their new book and entices orders.
The main function seems to be getting special offers in front of people without needing to alter the website dramatically. An example of this would be a company that's hiring but doesn't know where else to mention that on their page. So for stuff like this, it looks good, and the one thing I'd be interested in would be the option for a larger drop down that could show more than a single line but still looks beautiful (which your site currently does).
Thanks for your feedback-- I really appreciate it!