Just wow. As a species we have been on Earth how long, no society has ever eaten like that. Your instincts are correct, their method simply sucks, literally. If you base your meals on learning how to combine whole foods the benefits will be a natural way of eating that has sustainability built in.
As an alternative you could start with protein at every meal (my selection is animal meat or fish of between a third to half a plate), and some some low sugar vegetables and or berries. If there isn't enough fat in accompanying the protein then maybe some avocado, cheese or similar.