> I find it incredibly difficult to fool myself intentionally
I'd call it more recontextualizing than fooling yourself. Here's a science analogy:
As a toddler, you probably learned that the sun is up during daytime and down during nighttime. As an older kid, you likely learned that it rises in the east and sets in the west. The ancient geocentric viewpoint was that the sun goes around the earth. Ptolemy noticed that this doesn't match the observed data exactly, and so introduced the idea of "epicycles". A couple thousand years later, Copernicus discarded the idea of the earth as the center of the universe, and proposed that the earth revolves around the sun. Kepler refined Copernicus's ideas into the planets moving in ellipses, with the sun at one focus. Einstein then discarded the idea of having a central point at all, all motion is relative if you set up the correct metric tensors to model acceleration and gravity. But then if you ask a mathematician, Ptolemy was correct in the first place, his idea of epicycles was just a Fourier series decomposition of the observed measurements of the position of planets, and no more or less legit than any other mathematical model that explains the data. The math was just hard to work with.
All of these viewpoints are true, but they explain your senses in more or less detail, and progressively newer and more complex models are capable of explaining a greater variety of situations in greater precision.
The same with emotions. As a kid, the time your mother lost you in the mall was your whole world, because your mother was your whole world. You may have learned that big open spaces filled with crowds are not safe, and carried that forward with you as part of your model of the world. But the point of therapy is to contextualize that emotion, to realize that it was one time, and your life is very different now. You learn to feel it as an emotion, and as a memory, complete with context and everything else, and not as an unconscious rule of thumb that you need to live your life by.
> Also, the mechanism you explained implies that you could get rid of trauma by yourself any time you remembered the traumatic experience
You can! That's the amazing part. Once you've actually had successful EMDR sessions, you can learn the pathways to access your emotions, and just do it by yourself while you're lying in bed. There are apps for it too. And eventually, once you get adept enough at just accessing your emotions and feeling your feelings, you can dispense with the lights too and just recognize what you're feeling in the moment.
Now I just spend the car ride to work or back home decompressing and feeling all the unpleasant emotions that I bottle up during the day because it's my job. If you're doing it right, you can get rid of the therapist after a few years and become emotionally self-sufficient.