The trouble with this sort of recommendation [low- carb and paleo diets] is that it would take a large-sample double-blind longitudinal study to generate even weak evidence that the proposal actually increases longevity, and performing such studies isn't remotely feasible.

This is not true at all, and blindly worshipping the double-blind study like this will prevent you from learning anything. Dietary studies, with few exceptions, cannot be blind since people know what they're eating. But people can easily observe what effects diets have on them, as long as they're keeping the right quantitative data. Weight isn't the right variable to be tracking, since it can't distinguish fat from muscle, and many studies went astray that way. But tracking exercise reps, body fat percentage, energy levels and various interesting blood tests are all feasible, useful and actually done. A simple observational study plus an understanding of biochemistry is sufficient to justify a dietary preference, so long as certain known traps are avoided.

I won't mix claims about the goodness or badness of particular diets in here, but I'd like to say that the questions are answerable, and some diets are better than others in general. Individual biochemistries vary in ways that interact with possible diets, but those interactions can be understood, and many of them are understood, so it's wrong to point to individual differences as though they make diet inherently mysterious.