A high-protein breakfast results in less snacking. Why? Protein-rich meals prevent the secretion of the hunger-hormone ghrelin. Protein-rich meals also stimulate the release of the satiety hormone peptide YY. So, to put it simply, you'll stay fuller longer.
My standard go-to is a protein shake made with milk and a banana. And I can scramble 3 eggs as fast as my kid can pour a bowl of Frosted Flakes, so "I don't have time to cook breakfast" isn't really valid unless you cook fancy things, unlike me. So there's the "why" behind eating a high-protein breakfast. How one defines "high protein" is another topic, but a protein shake has more protein than a bowl of Frosted Flakes...totally in a rush, grab a protein bar (I keep a bowl of them on the kitchen counter...).