But even if the people will be confined, you have to be careful to take a broad enough population. I can expect people willing to participate in such study maybe are already orthorexic diet freaks? Or very poor people (which have a diet deviated from “mean”)
Doing studies with humans ist just hard!
The topic has changed from a study to a self selected set of people who want to lose weight badly enough they are willing to pay to be confined in some setting where they cannot access food outside of what is given to them, and they are forced to follow an exercise plan of your (not their) choosing.
You can of course study these people, but the only study anyone is interesting in is how different changes in conditions affect how much people lose and how much money you can get out of them.