Your argument essentially amounts to the following:

1. Melatonin significantly improves sleep quality.
2. It has no side effects.
3. It has low cost.

If all of these are true, then who wouldn't want to take it? However, you spend a lot of time on discussing point 3, but little on points 1 and 2, which are arguably the most important. How do you know that Melatonin really improves sleep quality so much? Is it just based on your personal experience (and perhaps that of other people you know)? If so, that is not convincing, as large scale randomized controlled studies are generally the only way to reliably tell if a medicine works. There are too many complicating factors like individual differences between people, the placebo effect, random fluctuation, reversion to the mean, difficulty in remembering how we felt in the past, etc. to rely on anecdotes.

Another point that your article does not address is the fact that there is a difference between a medicine having no known side effects, and a medicine ACTUALLY having no side effects. Any time that you take medicine you are taking a risk of a reaction that is unknown, or which failed to be uncovered in any studies that were done on it. For example, it is probably unknown whether a decade of Melatonin use (rather than just one or two years) causes problems of any kind. This sort of danger is unfortunately difficult to quantify, but I believe deserves at least some mention.