Don't quote me on this, but this is my understanding. A wider aperture lets in more light, which allows the camera to go for a faster shutter speed and/or a lower ISO. Meaning image capture will be faster and with less motion blur, and if you go for lower ISO the shots will look less noisy/grainy. Either way, this helps to take better photographs. Same applies for low light.
As Andrew Martonik from Androidcentral puts it:
"In photography, light is the currency you use to buy good photos. Even with other limitations like small sensors and lenses — like the ones in our smartphones — taken into account, you can always take a better photo with more light."
So more light is always nicer if you ask me.
The downside? Softer focus? If that can even be considered a downside. The wider the aperture, the less things will be in focus. You know those bokeh effect where the front object is sharp and the rear objects are blurry? That. Whereas for a smaller aperture, more things will be in focus and the background will be less blur. Just like how sometimes people squint their eyes to see things clearer. So for taking photos of landscape, a smaller aperture is prefer cause it will look sharper.
From Wiki:
"If an aperture is narrow, then highly collimated rays are admitted, resulting in a sharp focus at the image plane. If an aperture is wide, then uncollimated rays are admitted, resulting in a sharp focus only for rays with a certain focal length."
