Breathing through the nose filters, warms and humidifies the air. It supports a calmer nervous system and deeper, less fragmented sleep. It is the way the body is built to breathe at rest.
Breathing through the mouth does none of that.
And there is one more thing. During the growing years, the tongue's natural resting position against the roof of the mouth is understood to support the healthy development of the palate and jaw. When the mouth hangs open through the night, the tongue cannot rest there.
Over years of nights, that may contribute to how the jaw and palate develop. It is not a diagnosis and it is not a certainty. But it is a reason enough parents have started paying attention to what their child's head is resting on.