Huh? If I put a lightbulb above something, the place it’s above won’t have shadows, but there will be shadows at places that aren’t directly underneath.
Only places near the equator will be parallel with the sun. Anywhere else, because the curve of the earth, there will always be an angle, and thus even at high noon on the summer solstice, there are still shadows in Alexandria. So I don’t understand your analogy. It doesn’t apply because the earth isn’t flat.