I have gassers, charcoal grills and smokers (mostly but not exclusively Weber equipment.)
I have not done a side by side taste test to determine the benefits of charcoal vs. propane (or natural gas.) I would need to do that to assert that food tastes better cooked over charcoal. I do have the feeling that food benefits from charcoal but have no proof.
Likewise I'm convinced that a charcoal smoker like the WSM is far superior to a propane or electric smoker, but again I have no proof. I have heard claims that a stick burner or traditional pit is better as well. :shrug:
There is pleasure to be gained from cooking over wood or charcoal fire that adds to the total experience if not the flavor. I would not discount that aspect as it is an important part of the total. Would you go to a Greek restaurant that served Saganaki that was lit in the kitchen and brought out to the table after the flames subsided? It would taste the same, right.
The various fuel types have their uses and appeal and the wise cook will learn their characteristics so they may take advantage of them.
When I'm preparing dinner on the grill, I frequently grill my vegetables and that may take all of the space on the grill, requiring that I finish at least some of them before the meat goes on. What I've been doing lately is to put the gasser on low and warm the meat before putting it on the fire. (Think reverse sear.) Then the vegetables go on a cast iron pan on the gasser while the meat cooks. I did this recently with lamb chops and it worked great. It takes more skill than I possess to do all of this on one charcoal kettle.
If I'm just going to grill a couple vegetables, I fire up the gasser to do that rather than take the time to light charcoal.
Horses for courses.