A short flange distance does not automatically improve image quality by itself. Its main benefit is that it gives lens designers more freedom.

With the sensor closer to the mount, some lenses can use less extreme retrofocus design. That can mean fewer corrective compromises, sometimes fewer elements, smaller lenses, and potentially better sharpness—especially compared with designs that must push the rear optics far forward to clear a mirror box.

The trade-off is the one you identified: light can strike the sensor at steeper angles near the frame edges. Digital sensors generally prefer more uniform, less oblique ray angles, so this can increase edge shading or other edge-performance issues. Because of that, lens makers may still include a mild retrofocus arrangement even when a very short mount would allow otherwise.

So a short flange distance is mostly an advantage because it expands the design options; it does not force designers to place optics extremely close if that would hurt performance. It also makes adapting many longer-flange lenses easier. In practice, the mount itself is not inherently “better” for image quality—good results depend on how the lens is designed for it.