People who keep putting off writing don't want to write, they want to have written. Some people might actually enjoy writing if they started, but don't want to start.

When I have something that I want to do, then categorize it as something I "should" do, I generally want to do it less. Attaching the sense of moral obligation makes me forget that the original reason I put it in that bucket was because it was something I would actually enjoy doing. This seems to line up with your hypothesis that people conflate these two and cause problems for themselves. But this also seems to imply that there is, in fact, a relevant difference between "want" and "should," at least in one's own head.