Do you know how you lose weight? You lose weight by exhaling carbon atoms, which combine with the oxygen you inhale to form carbon dioxide. Whether these carbon atoms were previously bound to fat or sugar is irrelevant for weight loss. Your training only helps you burn more calories. With normal training volumes, weight loss is achieved through diet.
The real reason for training in Zone 2 is that you don’t tire as quickly and can therefore do it every day. If you do a high-intensity workout and burn 100 kcal more, but are then so exhausted that you can’t do your next workout until three days later instead of the next day, then training in Zone 2 is the better choice.