The Chuckbox is severely overrated. On the strength of its reputation, it was one of the first places I tried when I moved to Tempe. Over the years I've stopped by now and then to see if it had gotten any better. Nope, still the same boring burgers.
Char-broiling a burger over an open flame just doesn't do it for me. It always results in a dry, bland burger. Mesquite or no, it doesn't really make much difference when you're quickly broiling the burger. And it doesn't help much to pile on a bunch of junk from the condiment/topping bar--it just makes the thing a big mess. I'd much rather have a burger cooked on a flat griddle-surface like they do it at Delux and Welcome Diner. And when the kitchen applies the toppings for you, it results in a better melding of flavors with the rest of the burger.