I would say global illumination is best when you don’t notice it, because it should look natural to you. Without indirect lighting you would have pure black shadows. True, you can use a Skylight, but that doesn’t always work out that well. In outdoor scenes it mostly does, but indoors not so much.
Actually, if you would have the perfect global illumination the occlusion would be automatically be part of it. We do ambient occlusion because we can’t afford to do it the physically correct way through global illumination, it would be just too expensive. 
I tried to visualize what I mean by playing with Koola’s Lightroom scene: https://imgur/a/3DX8M
I’m not an artists and was thrown together fairly quick, but I tried 