It isn't though.
Sometimes, (a lot of the time) it's about fixing what is going on in the body first, because without that then a calorie deficit won't work anyway.
You don't seem to realise that a lot of peoples bodies are malfunctioning.
There are people who eat low calorie diets and they don't lose weight and their body shuts down certain things in the body assuming it's starving and it doesn't touch the fat that's there as an available source.
There are overweight people who go on diets but their body is malfunctioning and storing as much fat as possible even though the kcal would be better off used elsewhere in the body.
If cortisol caused the weight gain and someone is told to keep cutting their calories they're likely to get even more stressed which makes the problem even worse.
Your ‘whole list of reasons why those diets help’ are presumably to do with making the body accept living at a lower weight, aren’t they?
No, it's definitely not all about that at all.
A malfunctioning body doesn't feel healthy, it doesn't run in a healthy way, it's not all about weight at all, it's also about how a person feels etc.
People might often start a new plan to lose weight but many are sick of how they feel too, no energy, sluggish, sick etc.
From the trainers I know who consider themselves to be 'feeders' when their clients post their results sure they say the weight lost and inches loss was great but most of them say the biggest change was in my energy, motivation, mood etc. and write an even longer paragraph on all of the other benefits they got from it.
That means you aren’t constantly battling hunger while eating very little. That makes creating a deficit or avoiding a surplus easier.
It does seem to me that you and @Watchkeys want to play down the importance of hunger.
There's no need to eat very little though, and it's not just about battling hunger.
For a PT, ideally you want the client to feel amazing, to feel energised, healthy, motivated etc, to get a boost in mental health etc. as well as reaching the body goals they want.
Some will argue that starting to lose weight is what will give people the energy boost, motivation etc. and that's what makes them continue but I believe that's just a small part of it.
Inflammation messes with the brain as well as the body, so do gut issues....a drop in calories doesn't tend to fix those things and can make them worse, low calorie diets can wreck the gut and gut issues can be remarkably persistant.
It all depends on what is going on in individuals bodies. Apparently keto can wreck the gut for some too. Luckily keto did the opposite for me and cut inflammation,, reduced cortisol and helped my gut. It totally reset my body and fixed me. I felt amazing on it from very early on too so that was a good sign to continue.
Any trainer/nutritionist etc. who advocates the same approach for everyone and thinks it all boils down to just a calorie deficit is doing their clients a major disservice and could be harming them.