The most obvious problem with crash diets is that the weight loss is almost always temporary. If you suddenly change to a restricted diet, your body will respond by storing less water. You will lose weight and be less bloated, i.e. thinner, but you will not necessarily lose any fat. When you end the diet that weight will go right back on.
Of course, you may lose some fat too, depending on the diet and how long you follow it. However, the body often goes into starvation mode during these diets. It thinks a famine has hit, and it should slow down the metabolism and store as much fat as possible to guard against the hard times ahead. When you increase your food consumption, even if you do it in a healthy way, that famine metabolism can persist and lead your body to gain some or all of the weight back.
Added to that is the psychological effect of breaking a crash diet. Whether this happens at the end of the planned diet or in the middle out of desperation, it tends involve overeating. For this reason alone, many people who follow crash diets find that a month later, they are heavier than they were before the diet.
In addition, there are some significant health issues with crash diets. First, diets that focus on losing weight fast are usually very restrictive in the types of foods that you can eat. Many foods (and sometimes whole food groups) will be cut out. This is not something you could do in the long term without suffering from deficiencies. It is not good for the body in the short term either.
On many crash diets you will not be getting the nutrients that the body needs. It is true that you can take supplements, but many supplements rely on substances in whole foods to make them work most effectively. Nutrient deficiencies lead to cravings, making it harder to stick to the diet and more likely that you will break out in a binge. At the same time, you may be getting more of some nutrients than is healthy.
To summarize, crash diets can only ever be a temporary solution, for example for a situation where you need to lose a little weight for a particular event, and you do not mind if you gain it back - and more - afterward. The healthiest option for losing weight is to make changes that will allow you to lose weight slowly on a healthy eating plan that does not ban any foods completely, but allows you to incorporate occasional treats. In the long term, people who follow crash diets are likely to gain weight, not lose it.