From a mechanical perspective, a screen around the outside would create a wrinkle rather than a crease when opened, and that wrinkle would be substantial. The phone would need some sliding/rolling mechanism to pull the screen flat. Possibly doable, but finicky and fragile. Especially considering elements like cameras, touch ID, etc.

From an experience perspective, I imagine it's just more satisfying to open it like a book. A screen on the outside would mean the inside is almost empty, just utilities like camera lenses.