> The tune of Happy Birthday doesn't seem particularly catchy to me. We've just heard it repeated so many times.
Read the story. The authors actually did a lot of work on Happy Birthday. (They had a couple of conflicting goals and did a lot of testing.)
While short little melodies are trivial to write, HB isn't just any short little melody. Disagree? Come up with a few that work as well. Riches await.