No weed. Just think of the normal vectors on a flat surface vs. a round one. The flat surface has all parallel normal vectors. Check my ****ty mspaint drawing:
If the flat eye is at F, the direction of gaze is Y, and we take the limit of X towards infinity, then the angle at F converges to 90 degrees. But at 90 degrees the eye is not looking at the point, it's looking above it. For any given angle below 90 degrees, the vision of the flat eye is gazing at a finite value, it cannot see the point at infinity. A flat eye can never "see" a point at infinity, it's not possible to create an angle where it lies in the field of view.
The curved eye has no such issue. As long as the edges of the vision are around the point at infinity, there exist plenty of angles at which the point the line converges to is within the field of view.
It might have something to do with the measure of your field of view: with a flat eye, the further you look the proportion of what you can see drops to 0. With a spherical eye, you maintain the same proportion no matter how far you look.