I genuinely don't think anyone means the same thing when they say traditional smoke flavor. Especially among BBQ casuals, but even among enthusiasts.
You get a different flavor profile from the method used. Charcoal and smoldering wood chips will taste different than gas or electric and wood chips. Charcoal and smoldering chunk will even taste different than charcoal and chips.
A pure burning wood fire on a 900 lb smoker with correct draft will taste different than a pure burning wood fire that is choked from oxygen.
Pellet grills taste the closest to a clean wood burning BBQ. They don't taste like the other methods that use more charcoal and smoldering techniques. Do pellet grills taste as good as a perfectly managed all wood fire? No, but they are a lot closer than I think a lot of people say they are. I spent years perfecting a clean burn technique on an offset smoker. Using small splits that reached total ignition quickly. BBQ made with this technique tastes very close to what you get when you use a high quality big flavor pellet like hickory. You can tell the two apart, but if you were asked to rate the smoke levels (not flavor, just smoke amount), you'd put them about the same.
Based on that, when people say they aren't getting enough smoke flavor, I automatically assume that they are looking for the charcoal / smoldering style flavors.
There is nothing wrong with that mind you, just that it helps to be more specific in the type of smoke that we want. Personally I like both styles. I enjoy a heavy charcoal oxygen deprived short smokes like pork ribs. I think Kamados make the best pork ribs, but vastly prefer an offset or pellet for butts or briskets. Just my personal preference, there is no wrong answer here.
But we should call out that thicker white smoke from smoldering wood, or flavors we get from charcoal are not what you would call traditional BBQ flavors to be honest. If you told that to a "traditional" pit master, their eyebrows would go up. Heck, "traditional" east coast pit masters don't even burn wood in their smokers, they pre burn it and transfer the hot coals to a fire box or a ground pit. I've been to many of BBQ joints around Texas, some small and some famous, and almost none of them have that wood smoldering flavor, they are all closer to the all wood, total burn flavors. I only mention this because it helps to have a "palate" of the different types of smoke profiles out there, and that may help you adjust expectations that you are or are not getting enough and what to do about it.
Just my .02, and my advice is to play with your pellet choice, and spraying the meat more to get the smoke to stick.