Why do Egyptian figures stand sideways with a front-facing chest?

Because Egyptian art was not meant to be realistic. The ancient Egyptian language had no word for "art". Artworks served a function bound up with religion and ideology, and to render a subject in art was to grant it permanence, so the world they portrayed was idealized and unrealistic, drawn by a set of rules.

The best-known rule governs the human figure. In relief and painting, the main figures have the head and legs seen from the side, but the torso seen from the front. Another rule fixed the proportions. Figures were measured in 18 "fists" from the ground to the hairline, a convention visible as early as the Narmer Palette.

Size did the work of rank. Gods and the divine pharaoh are drawn larger than high officials or the tomb owner, and servants, entertainers, animals and trees are smallest of all. So the artist's job was not to invent but to comply: works were ranked by how well they obeyed the conventions, and the conventions were followed so strictly that, over three thousand years, the appearance of statues changed very little.

One reign broke the pattern. Under Akhenaten, Amarna art was the most drastic interruption in the style, and after his death artists went back to the traditional styles.