News to me, I was always under the impression a Maillard reaction occurred with reducing sugars, I don't know where you find them in protein and fat.
Certainly, steak will brown with cooking. Or even before. However, it's not a Maiilard reaction, it's a myoglobin oxidation.
I don't bother buying steak in Thailand to eat as is, I put gravy beef in curries instead. Nothing tender here.
In Australia, I use grass-fed eye fillet with a hot pan lightly coated with oil. Sear one side, then the other. Turn over one final time, then wait until liquid forms on the top of the steak.