The external side shields also server to intercept radiation and convert it into heat. Radiation traveling through the air doesn't heat anything until it hits an object. When radiation hits an external side shield, the shield is heated and then that heat can be pulled off passively as in the BK by convection of the air rising between the shield and the side of the stove, or actively as in the Liberty and the Buck 91 by the blower moving air between the side and the shield.
It would be interesting to have the side shield off the BK, then shoot all over the side with an IR gun, both toward the front where the shield stops and the flame and coals can radiate directly into the sidewall of the stove, and further back where the side is complete shielded from radiation of the flames and coals. I'd like to see what the different temps would be. I think the inner shields probably serve to intercept radiation off the coals/flames and keep it in the stove, as opposed to letting it hit the stove walls and allowing some of that heat to leave the box. That may allow the cat temp to stay up at lower burn rates. Now, that heat should eventually leave the box, but is probably best stripped at a low burn rate where the heat doesn't go up the flue, but has a chance to get out the top of the stove. I think that stoves that allow more radiation to the walls, and have blowers that cover the side walls, will get more heat out of the box, faster, at high burn rates than a BK will. It all comes down to engineering decisions.
As has been stated here, all stoves operate on a combination of radiation and convection, and the two are inextricably linked.