Here are some of my thoughts on the topic.
I think this is a very good question, and it's a difficult one to answer. I also sometimes struggle with whether we really need to analyze the literature in-depth. I can think of a couple of benefits:
1) Literary terms are another part of the "common frame of reference" issue. If you have a conversation with another person about a book, it is easier to talk about it if you both understand certain terms. Terms like plot, character, and theme; conflict, climax, resolution; simile, metaphor, personalization, and even anthropomorphism, can help you explain what you did or didn't like about the book, and can enable you to discuss the book much more effectively.
2) In a similar way to your son's development of interest in the topic of Mrs. Giaconda, a grasp of literary terms can generate interest in areas he may not have been interested before. It can enrich your understanding of the story of Eros and Psyche, for example, to recognize similarities in the plot between that and C.S. Lewis' book, 'Til We Have Faces. Analyzing the similarities and differences in the plot and theme of the the two stories can also help you understand Lewis' theme much more clearly. Can you manage without knowing that? Sure! But does it enrich your life, in some small degree, to understand Lewis' theme in his story? I find that it does.
The point, of course, is not the little tiny bit of additional richness we gain from any one experience with literature (like your son's experience with Mrs. Giaconda), but rather the enormous wealth we gain from the accumulation of many such experiences over time. That's also why any one piece of literature is relatively insignificant, but a wide exposure to literature over time and across cultures is important and valuable. (I think that's why you may hear people say that if you don't like, for example, The Second Mrs. Giaconda, skip it and find something else; but don't skip literature or the study of it altogether.)
That said, I want to make it clear - I don't really think worksheets are all that significant to the process. The discussion of the literature is far more important than
filling out the worksheet. If it's more comfortable for your son, make a list of significant literary terms and features (maybe with definitions), and have him choose the ones he feels are important in this particular piece, point out examples, and/or explain why and how he feels they are important. When you find he's consistently leaving out some of them, choose a piece that contains "x" term, point it out to him, and talk about it. This of course demands more of you as the teacher, but it may be more effective for him. Or, just do the worksheet questions orally. Find a way that works for you and for him to consistently discuss the literature using literary terms. When I was using discussions in teaching literature, I always found I learned far more than my students, and I got far more meaning out of what I had read than they did. The more deeply you analyze, the better you understand the literature as a whole, and the more you usually end up appreciating it in the long run.
Finding the interesting things in literature and figuring out how to communicate that to students can be one of the most challenging things about teaching literature - but in the end it can also be one of the most rewarding.