I would not guess that foiling has anything to do with the type of smoker.
A offset stickburner has a totally different air flow characteristic, and that is all the difference in the world in how the flavor builds in the meat. Now, I doubt, given a skilled WSM guy and a skilled Off-set guy that I could blind taste the difference. But, you use different amounts of wood, because the smoke drafts over the food differently. A side burner moves a lot of smoke carrying air over the meat, but, it is moving quickly through the cooker. A WSM is a much smaller cooker, and with a vertical draft, the smoke hangs around the meat a bit more. That all makes a difference.
I suspect the foiling was more about getting through the stall and controlling color. It has a negative effect on the smoke flavor, and thus, I doubt that is why folks went to it. It does make timing the cook a lot easier and controlling the color a lot easier. And we all know, a braised piece of meat is almost always going to be more moist.
I'm feeling bearish, and I'm packing a Wusthof Grand Brisket slicer from MABA
"I'm Armenian...perhaps...but then again...maybe not..."