https://nothings.org/gamedev/ssao/IMG_0064.JPG
You can see a sharp shadow near the door frame. So yeah, ambient occlusion is not going to simulate that, but it was never supposed to?
It's supposed to make 3D shapes look good without the need to place lights or do more complex ray tracing. It roughly approximates what you could perhaps see inside a photographic lightbox. Light is coming from every direction and every surface is matte.
The reason it's used in computer games is not that it's photorealistic under all lighting conditions. It's that it makes geometries look better than before with less computational overhead than the alternatives. Harsh lights often look nasty and diffuse lighting is expensive.