Soft focus around the edges is common in lower quality lenses. This is because it cost a lot more to manufacture a lens that holds sharpness all the way to the edges, and the selling price has to justify the manufacturing costs. In professional camera lenses, edge sharpness is a sought after trait, and they are significantly more expensive than the consumer lenses. These little action camera lenses just can't command the price of exceptional focus edge-to-edge. I'm not trying to sound authoritative here, so please don't take this as gospel, but if I remember correctly, a wide-angle lens is easier to produce with a better apparent edge-to-edge sharpness. If I am remembering that right, then it makes sense that as we change out our original wide-angle GoPro lenses for longer focal length lenses in our scope-cams, the edge sharpness fall-off would be more noticeable.
As for what 2fast was saying... I both agree and disagree. The scope is going to produce an image of a given quality. That image was engineered to be viewed by the human eye through the fixed optics of that particular scope. When we add a scope-cam, we are adding multiple optical factors (a beam-splitter and a lens that both degrade the image and the amount of light passing to the final sensor). These elements were never part of the scope design, and this will almost always detract slightly from the original scope image quality.
I agree that changing the scope will not correct factors inherent to the scope-cam system that we added (light and focus fall-off toward the edges, beam-splitter, etc), but if you change scopes and that significantly changes, for better or worse, the starting image, you should see a similar change in the recording if the recording system is the same. I feel pretty confident that if you use the same scope-cam setup on a $250 scope and a $2000 scope, the recording from the scope that produces the better starting image is going to have the better recorded image, regardless of how much degradation the scope-cam introduces.
A scope-cam recording is actually the sum of two independent optical systems. Increase the quality of either or both of the two addends, and you will increase the quality of the sum. The reverse also applies.