I'm always on the lookout for that sort of thing too, but I don't think you're right here. I get annoyed when people say "ellyagg likes to program" because it's dismissive, like I'm some strange creature who finds the task of putting various glyphs in parallel lines soothing. I don't enjoy programming for programming's sake. I enjoy creating and I enjoy my creations bringing value to other people's lives.
I guess I don't interpret "like to program" that literally.
I think it's accurate to say "I like to program" because it goes beyond problem solving for me. I enjoy solving the problem, yes, but I also enjoy expressing the solution. I enjoy the process of figuring out what is the most concise, elegant and natural expression of the solution, and I find the result pleasing.