That depends. I've visited plenty that use a Mesquite or charwood fire. THE Steakhouse at Circus Circus is a great example.
I like using the high heat of wood chunks even more so than charcoal; see below.
Quite true, but, at least based on my experience, they are somewhat less likely to be found, especially amongst high end restaurants. I suppose experiences will vary, truth be told, I don't much care how my steak is prepared as long as the person doing it is highly skilled and the final product on my table looks and tastes great.