Then technically that's not grilling, that's just trying to use a grill as a poor excuse for a smoker. By strict definition grilling is done without a cover while smoking and real BBQ is all about low temps, lots of time and smoke.
Grills best serve as grills and purpose built smokers always make better smokers.
I have a smoker grill but have modified it so now it isn't much of a grill at all. I have a small grill that I use for grilling up steaks and such. I could still force the smoker into the grill role but why? It's like using your car to haul a load of gravel, you can do it but it doesn't make a lot of sense and isn't much fun. Using the right tools for the job always helps to ensure a that a good job and outcome results.
I can't imagine fiddling around with a grill, even a
Weber kettle, for the hours it takes to do up a good brisket. Lid off, lid on, lid off, lid on. How do you maintain any kind to temp like that? Way too much work and aggravation when Weber also makes a decent smoker for so cheap.
I say if you wanna do brisket? Then get some kind of a smoker or stick to steak, burgers, sausages and hot dogs or even poultry. But for those cuts that take a lot of time, like brisket and pork butt, get yourself a smoker.
Besides as anyone, at least any man, can tell you, one can never have too many toys errr ah tools.