Burgers cooked at a lower temp , say 350 on pellet grills are quite tasty. They pick up a decent wood fired flavor IMO. I tended to lean the way you described but have tried other ways much to my enjoyment. I get bored and like to mix things up sometimesI don't smoke burgers, because I think they taste better cooked high and fast, e.g. grilled, rather than slowly. Smoked MR, they come out with a texture like they were steamed.
Instead, If I want to add natural smoke flavor to burgers is by smoking garlic or onions.
Smoke until about half cooked. then mince them up and mix with the ground beef, along with egg, salt, pepper, and Worcestershire. Then grill or sear.