This course was very helpful for giving me a breadth of exposure to various ways to look at evaluating recommender systems. Having faced a very similar problem evaluating a recommender system for a legal document search/suggestion engine (like Google News for lawyers), this gave me a proper "birds eye" perspective on that problem that I wish I had before. We faced exactly the same problem you describe of finding the proper tradeoff between precision and recall, or search vs. discovery.
BUT what is lacking here is teaching us how to go implement these different evaluation metrics in practice. Sadly I don't feel any more equipped to go back to that legal search engine client and guide them toward a very concrete decision about the right metrics to use. I would just come with a mix of new opinions of metrics they should consider -- but how should they choose? what offline evaluation should we do? what online experiment could we run to decide? etc. If you had run us through problem set/assignments involving real-world situations like this, where we had to calculate these different metrics (given sample data) and come up with compelling cases for different metrics to use for evaluation, I would feel otherwise.
That said thank you for your hard work putting the course/specialization together. I hope my feedback helps constructively, but don't see it as criticism. It's because I am very enthusiastic about what you've been teaching me -- and I plan to go implement it for new clients of mine in my Data Science consulting practice (www.waterwaydata.com) -- that I only want the course to be the best it can be for others too.