There are a couple of things that make me sad about this article, and I’m on the run so I’ll only make a few points.
One is the implied greed of the reader: „They [thank-you notes] improve the frequency and quality of the gifts you receive.” As if expressing gratitude was intended to yield gifts! Maybe for someone, but that’s far from my reasons to say thank you.
Also, the formula that is guaranteed to „never fail” makes a number of hidden assumptions, e.g., that the gift is meant to be used (point 3). What if I live far from sea and get a stone from the ocean from my friend who’s just returned from there? What I’d like to say is: „Dear John, thank you for the stone. I like to think that you had thought of me as you picked it up. When I look at it, I think of you and how important part of my life you are. Thanks for being it.”
There are better formulas. Ones that work for me revolve around non-violent communication: read up Marshall Rosenberg or „The Power of Gratitude” by Liv Larsson for details.
Writing thank-you notes fills me with such an intense dread and self-loathing that I've generally tried to avoid occasions on which others would give me gifts. One tip I recently discovered, aside from having my wife dictate the text of the note to me, is to actually make 6ish-second thank-you videos. It is a lot easier (for me at least) just press record, enthusiastically say what is in fact a short message, and send it with a speed that prohibits you from getting caught in some weird spiral of thought.
Also useful but notably absent from this article – brevity.