You don't want that sort of starvation - if you want to lose weight, it needs to be done gradually. Otherwise, you lose muscle as well and you can't really live a normal active life. Go running three times a week and plan your meals; that should work better.
It's not starvation.
The main problems of starvation are dehydration, vitamin deficiencies and muscle loss from protein break-down.
If you're still consuming a balanced 7,500 calories a day and drinking water you'll be fine.
The exercise will make your body retain leg muscle. The body will break down adipose stores for extra energy.
How do you think running and planning your meals works? The exercise and better calorie intake causes the body to break down fat as well. The difference between a healthy weight-loss plan and starvation is not the calorie deficit, but exercise and vitamin intake.
Since hiking and eating involves both exercise and vitamin intake, the major threat is dehydration. That is easily avoided. Another problem is that a fat person is probably unaccustomed to the strain on his feet, and will develop blisters and might get lost. A map and some training walks will help.
I'm not claiming that everyone should go hiking, nor that it's perfect. It is, however, quick, not much more harmful than any other weight loss programme (in conception, anyway; when exposed to apathetic people any well-devised plan can be spoilt), and not at all akin to starvation.
Of course people should run three times a week and eat nutritious meals. People should also file their taxes on time, not get into trouble, never have raging arguments with friends and family and so on...
but sometimes people want slightly more effective solutions than simply to wish that all the mistakes of the past had never been made. A few days of hiking with a calorie deficit is simply accelerating the process of running a few times a week and eating a slightly reduced diet. I'm not advocating dropping any of the healthy factors, like vitamin intake, so I don't understand your violent dismissal of the suggestion.
The body is a remarkably adaptable thing. If you're hiking all day you can be suffering a marked calorie deficit and still retain muscle mass. The body responds to stresses and strains put apon it: bones and muscles grow and shrink as they're used, every day and night.
If you give it enough vitamin and protein to maintain healthy organ and nervous system function you can leave the rest to work itself out, and a 2,500 calorie deficit out of 10,000 or 7,500 is not extreme enough to interfere with the incredible adaptability of the body.
This I have experienced personally, I can guess at from my own research (not in this field) and can also be seen from any number of historical examples.
Being obese is grossly unhealthy; the lasting effects of a small period of starvation, even if it were to occur, can hardly compare unless organ failure is induced, before which the hiker will experience diarrhoea, vomiting, and so on: easily recognisable signs of illness.