A rotary shutter does not inherently create uneven exposure across the frame.

The key is that although points farther from the rotation axis trace a larger arc, they also move faster in linear terms. Linear speed increases with radius, so the shutter edge sweeps across those farther points proportionally faster. In effect, the greater distance and greater speed cancel out.

So while one part of the frame may begin exposure slightly earlier, another part will also be covered earlier as the shutter continues rotating. If you follow the motion through the full cycle, the bottom is not simply exposed longer than the top; it is also closed off sooner. The total exposure time remains effectively the same across the frame.

This is the same general idea behind why rotating shutter designs can provide a consistent exposure interval defined by shutter angle and rotational speed, rather than causing a brightness gradient across the image.