You did a great job in zooming in on the key variable: What people mean by "works."
When people talk to me about my diet, and start in with what "worked" or have some evaluative framework, or ask why they should eat either the way I eat, or vegan, or vegetarian, I feel I need to contextualize the discussion. Usually I ask, "What do you want to accomplish?" Then I tell them what I want to accomplish: Live longer, not become debilitated as I age by diseases caused by diet, not suffer pain as I get older from diseases of deterioration or organic failure (arthritis, diabetes, congestive heart failure), feel fit and without avoidable physical limits, and die a short and late death, not a long, drawn-out and painful deterioration ended by either a painful hospital bed stay or a traumatic episode with the feeling a elephant is sitting on my chest.
I don't ask for much.
Losing weight is a bonus, but it is only a factor because of the first 40-some years of my life eating a SAD.
But if losing weight is it--and for most people, I think it is, at least initially because that weight is the only visible symptom, and thus the only acknowledgeable symptom, of their bad and deteriorating dietarily induced health--then lots of stuff "works," and low-carb does too. Note that virtually no one (there are a few exceptions) says, "I know that John/Judy lost 40 pounds and has never regained it after 5 years." They talk about someone who has lost a dozen pounds in the last few months.
Well, that's easy: Water loss from a dehydrating diet; glycogen depletion from a diet lacking enough carbohydrate to keep the body energized. Boom, minus 12 pounds. And plus enervation, acid reflux, inability to concentrate, bad sleep, corpse-decay breath, accumulating fat deposits in the circulatory system, and accumulating body fat.
It "works." Because all they measure it by is one thing: Weight. True, no one can limit the effects to that one thing; you can't do low-carb and lose weight and not get the rest of the effects. But that's not what they want, so they don't look at those things. Until one or more of the other effects become so bad that it makes the weight loss drop in importance below the new pain they've brought on with the diet. (For my wife, when she tried Atkins, it was the acid reflux--which also made sleep impossible--and the constant mental fog.)
So maybe ask "What do you want to accomplish?" And if it's just "to lose weight," ask: "Why do you want to lose weight?" If you can drill down, maybe you can get to "to be healthier." Then you have a better way in, if they can say themselves what their deepest goal is.