With regards to regaining weight, As shown by Emeritus Prof. Keith Frayn (Human Metabolism) experiments at his Oxford lab, this is more to do with adipose tissue health (being the second largest endocrine organ), its apoptosis/turnover time as well as insulin sensitivity (as evidenced by Chris Gardner's study out of Stanford).
The issue is you do not consume calories per se, but rather food which is broken down into a host of amino acids, fatty acids and saccharides that illicit varying hormonal responses (critically insulin, glucagon, leptin, ghrelin and the incretin hormones) within the human body (that then dictate fuel partitioning, cell autophagy, metabolic/catabolic responses) are therefore not solely dependent on calories but rather the nature of macronutrient intake. Depending on a whole host of genetic, aging and lifestyle factors, over time this causes metabolic dysregulation which presents as obesity and in most cases T2 diabetes.
In addition, refer to the work of Prof.Ben Bikman where the absence of elevated insulin converts white adipose tissue into brown adipose tissue which
is akin to a slow wood fire that consumes energy at a cellular level over and above your BMR or TDEE.
Here is a list of some RCTs with some caveats:
1. It is critical to distinguish fad diets with basic human physiology. Everyone produces ketone bodies. The only important frame of reference is quantum. Carb fueled individuals typically run 0.2m/mols plasma levels. Individuals that have become fat adapted range from 0.5-5 m/mols. A prolonged fast will tip up to about 7. Once you go into high double digits, it is classified as ketoacidosis which is deadly. Basal insulin levels in all individuals (except for Type 1 diabetics that require exogenous insulin) will prevent that from happening.
2. There is no one size fits all optimal diet and I am not asserting that everyone should follow a well formulated ketogenic diet. However, for most individuals with metabolic dysfunction and/or diabetes, it is certainly the most prudent in helping deal with the root cause as well as co-morbidities. Chris Gardner's study out of Stanford proved as such. The critical factor is insulin sensitivity. I would also recommend the Virta Health Study (by Drs.Phinney, Volek & Hallberg) and Dr.Westman's clinical work over the last 10 years at Duke/HEAL clinics.
3.Whilst Double Blind RCTs are the gold standard for pharma research, it can be argued that nutrition science is an entirely different kettle of fish. Whilst you have separate cohorts acting as control/placebo and target groups in drug trials, removing a macronutrient long term within a metabolic ward setting is extremely difficult, incredibly complex and prohibitively expensive. Omega 3 v Omega 6 for example are both critical nutrients but an equally important part of the equation is the ratio as both serve different functions in the body and all foods contain a mix of macronutrients.
There are some RCTs here for you to check out:
https://phcuk.org/rcts/