I'll be up front - I do disagree with your take, at least partially. I quite like the screwdriver analogy used elsewhere in the comments.
I love working with computers. I have for years.
Recently, I turned that into a job. I enjoy my job, though I wouldn't say I love it. However, it does allow me 5o practice and learn, so that I can improve my skills when I do perform a labor-of-love project.
If I were to make a labor of love project, and then someone were to pay me to support it, why would that project atop being a labor of love? There would be extra workload that would not (billing, other business cruft, etc), but I think the core of it would be.
Similarly for art/music - if I producea song because I like writing music, and people are willing to pay for a high quality download, would it stop being a labor of love at that point?
Curious to hear your thoughts on these edge cases.