I did a quick search on google scholar.
There are loads of published peer reviewed studies about diet comparisons. Most of them have contradictory conclusions.
You can find a peer reviewed published study to prove pretty much anything, especially if you only read the synopsis, cut from that and draw parallels to situations not actually tested within the study implying that it somehow supports them.
I found a study that said: low carb, non-calorie restricted diets appear to be at least as effective as a low fat calorie restricted diets over 1 year.
Note, “at least as effective”, not “more effective”. The results were broadly the same, just a different route of getting there.
Of course back in the real world where actions aren’t as controlled as they are in a study, the most successful diet will be the one that works (not necessarily that works best), and is easiest to stick to. Not the one proven most effective by a tightly controlled clinical trial.
I strongly suspect that this is where the idave diet succeeds. It works well, and because it makes your food choices for you it is relatively easy to stick to. It is easier to avoid a “bad” food group altogether than it is to eat it in moderation, that is just human nature.