I would love to know how many omelets I made during 2 years working breakfast. That said, expectations were very American style. A little water to make them fluff. I am not sure the methods I was taught conforms to anyone's best practices. That said, I love omelets, respect J. Pepin, and have cooked maybe 2 or 3 french style omelets, all at home following his techniques book (iirc).
To my taste, browning is to be avoided.
This advice is worth even less than what you paid for it.
We pre beat eggs, but not for fluff.