I'm afraid you still fundamintally misunderstand the study.
You're talking about a study with control groups, or a comparison study (formally called a "Randomized Controlled Trial," or RCT.) This would be a good design if they were asking the comparison question, "does a low-carb diet cause more weight loss than a low-fat diet," or something like that. Or if they were asking, "does a low-carb diet cause weight loss," they'd also include a control group (i.e., people on baseline diet that stay on baseline diet.)
But they were not asking either of those questions.
This study was funded by a group that already believes that a low-carb diet leads to more weight loss than other diet, so they are not asking that question! The group had a specific theory to explain why a low-carb diet should do better. Confirming their theory relied on very fine measurements, so they designed and funded a study which uses the necessary (and very expensive) procedures to get those very fine details, in hopes of confirming their theory. This study was basic experimental research, not an RCT, and this was not a flaw - it was an intentional design. There weren't comparing or testing... the were experimentally analyzing.
You seem to be confusing a control group with a baseline measurement.
If you're doing a comparison study or RCT, you need a control group. But if you're trying to measure effect size, you don't want or need a control group. A control group would be a waste of time. But you DO need a BASELINE.
For example, if you wanted to ask the question, "how much does blood pressure rise when a healthy is given an epinephrine injection," you don't need to waste time and money taking a control group that isn't given an injection. You need to give people actual injections and measure their blood pressures.
Of course, to know how much their blood pressures rose, you'd also need to measure them before the injection. That's where the baseline comes in.
The reason for the baseline diet in this particular study was because it's not enough to say that, before the study, these people were eating "normally." There is no normal - people eat all kinds of diets! So they have to be given a specific "normal" diet to establish a solid baseline from which to measure the small changes than can be measured in an expensive metabolic ward study.
To use an analogy, you're addressing by talking about a sensible study design for the question, "which can be thrown further, a football, or a baseball?" But this study was trying to answer the question, "is it true that the angle of throw for a maximally thrown baseball is just under 45 degrees from the vertical, and if so, exactly how much farther does it go compared to 45 degrees?"
To answer the football/baseball question, you just need a couple of throwers and you measure distances. You don't care about angles, at all, and it should be obvious which does better.
But for the other question, you'll need some sort of setup to capture the throws in a way that allows to you carefully measure the angle, as well as the corresponding speeds and distances. And you'd wan't to establish clear baselines for things like strength of throw and the wind at the time of the throw. And you wouldn't care at all about the numbers for a football, because that wasn't what you're asking about.
Does that make sense?
One more thing I think you're missing, but which is outside my main points... you said that if the study were 50% kept on baseline and 50% put on intervention, that
A metabolic ward study doesn't care about external conditions - in this kind of work, the internal conditions are as perfectly controlled as possible so that all you're measuring is the intended aspect, and the outside has no influence.
But just as importantly, you seem to have the idea that they'd put dozens of people into metabolic wards at once. That's not realistic. Metabolic wards are scarce and expensive, and only one person can be in the chamber for the entire period. A facility doing the work would likely have one or two chambers. If they have two chambers and 20 study participants, they can only run 2 participants through at a time. They'd need ten days, plus reset time in between each. They can't test everyone during "the same weather."
Putting someone through a prescribed-calorie trial for a month were every meal is provided is very expensive, and putting people through metabolic wards is expensive. If you only have enough money and time to put 15 or 20 people through, you're not going to have half of them skip the intervention. There's no point in doing that, and all you do is lessen the statistical accuracy of what you learn about the people who do experience the intervention you're analyzing.