Why not possible to register low carb diets like 2:5 or 1:1 or a day of fast ?

Regarding the discouragement of fasting... the American Medical Association and many other professional orgs are still using outdated science and research when it comes to fasting. For example, there are now 1000 of examples of humans reversing Type 2 diabetes simply by proper fasting. However, practicing doctors risk getting sued if they recommend fasting because it is still against the standard of care. The MYP team is following medical practices that say fasting = starving, which is horrible advice, but still the mainstream advice from doctors.

The truth about fasting is that human beings were designed by millions of years of evolution to function on ketone metabolism. If humans had to eat every 24 to 48 hours, then the human species would be extinct. If the human body started breaking down after 2 or 3 days without food, then how would early humans ever catch the food needed to survive? After 72 hours of fasting, you are more alert, your senses are sharper, and your muscles are primed for action. All of the biological systems a human needs to find and hunt food are maximized when the body is in full ketosis.

On the maintenance issue... you are a victim of The Biggest Loser syndrome. Calorie restriction does not work and calorie in-calorie out is a plan for failure. This is why all the Biggest Loser contestants gain the weight back. It is NOT a sustainable practice.
(This is also explains how a trainer from the Biggest Loser (Bob Harper) suffered a heart attack in 2017. CICO does not work for weight loss over the long term and CICO results in more health issues than fasting. CICO tends to cause health issues whereas extended fasting will actually correct a number of different health issues, including many of those caused by the CICO lifestyle. Some authors blamed Bob's heart attack on excess proteins (lipoprotein(a)) causing plaque in his arteries, but it is far more likely the plaque buildup started with insulin resistance of the arterial walls, which leads to the concentrations of plaque buildup.)

When you reduce calories, you cause your glucose metabolism to slow down. If you are eating once or more every 24 hours, then your body is always in a glucose metabolism. (If you have insulin in your blood, the fat burning mechanism (lipolysis) is actually shut off.) So, the minute you stop the program and try to eat regularly, your glucose metabolism will bounce back to what it was before.

However, when you are eating FULL meals and fasting for more than 24 hours, the body transitions from a glucose metabolism to a primarily ketone metabolism. (The brain still needs glucose, which is produced by glycogenolysis and gluconeogenesis.) So, your glucose metabolism is functioning at full capacity when you eat, then the body transitions to ketone metabolism without downregulating your glucose metabolism. This way, when you eat again, there is no upregulation of your glucose metabolism and the weight is much more likely to stay off.