Speaking on behalf of a family that's run Vietnamese, Chinese, Japanese, and Thai restaurants - It's just not a wok if there are no flames shooting around the sides of it that can sear the food as it get tossed about.
On the one hand, you do really need to be dumping a bunch of heat into the pan, and on a gas stove "flames shooting around the edge" is probably a good thing to look for.
But I don't expect the flames themselves actually interact with the food in a meaning way compared with the hot metal.
>But I don't expect the flames themselves actually interact with the food in a meaning way compared with the hot metal.
Maybe not as much as the hot metal, but they absolutely can (and should, under the right circumstances). See how these noodles are tossed over the flame? https://youtu.be/oX62hKkcb6s