I will admit when I am wrong. It looks like that method would work. I have been around the computer building community for 20 years, and I have never even heard someone even mention that method.
However, I wouldn't have the patience for that when a cloth and a little alcohol works so well, is so cheap, and gets the job done quickly every time.
Different strokes for different folks, I guess.
The only thing that will thoroughly clean the surface is a good solvent, and the only good solvent for this task and the cleaning of various other electronic parts is isopropyl alcohol.
However, I wouldn't have the patience for that when a cloth and a little alcohol works so well, is so cheap, and gets the job done quickly every time.
I think you missed where I wrote "usually".
For example https://www.amazon.com/Hosa-D5S-6-DeoxIT-Contact-Cleaner/dp/B00006LVEU/
I should clarify that I remove the majority of the TIM by scraping/wiping it off with something (old credit card, dry Qtips, a cloth, whatever) and only use the Scotch® Magic Tape to do the final cleaning. It pulls all the stuff out of the small micro-grooves on my Noctua D14 as well as whatever else might get left behind from the Qtips or other stuff that was previously used.