The earliest TV's had round CRT's that were masked off to provide a rectangular picture.
AFAIA oscilloscopes still do.
And I'm thinking you are on the right track.
The film/sensor is making an image from the light which hits it and that light is a "sweet spot" out of the center of the lens.
Thinking it through further, if the front element were square and properly convex it would have to be cut from a round blank to begin with which, again, would make it more expensive to build.
Next problem, all of the inner elements would have to spin as they turned. Being they are not round this would induce numerous balance issues.
Lastly, the film nor the sensor are square, they are rectangular.
Now, if we had a rectangular lens front element it would have to remain in a fixed orientation with no front element rotation ... nor could any of the other elements rotate.
In reality, I assume this could all be worked out but we would be left with a lens which was much heavier, much more expensive, and much more problem prone.
I'm not a lens maker, but I do have some mechanical backgrounds and those are the issues I come up with as I think it through.
The modern lens is an elegantly simple design and I doubt that it can be easily improved upon at this point as far as the internal focus mechanisms go.
LWW