What's missing here is what seems ALWAYS to be missing. We talk a lot about stuff the eye can't see, like differences in resolution that can only be revealed by controlled tests. That stuff is IRRELEVANT! Let's deal with stuff we, with our imperfect eyes, can actually SEE!
With no negative in your carrier, focus the edges of the frame, and stop the lens down rapidly from wide open. You will see that the center darkens rapidly, but the outer part of the field doesn't begin to darken until the lens is stopped down considerably, at least one stop, more likely two. This will look very strange. If you plucked one of your eyeballs out and laid it in the corner of the easel, looking up at the lens, it would NOT see a circle of light. However, were it to be placed in the middle of the field, looking up, it would see a round circle of light. What we are talking about here is "cutoff". From the corner, seen wide open, the light is cut off by the front of the lensmount and on the other side, the rear. Lenses are mounted in a tube. If you want to have an even field with the print not getting overly light in the edges and corners, it is necessary to stop the aperture down to where the open area is entirely enclosed in the part of the lens that is NOT cut off. This usually means at least f/8. That is where I instruct MY students to start, and to go down from there, not up. If this isn't clear, hold a toilet paper roll tube up to your eye, and while looking through it, rotate it a bit off axis. You will see what I mean. So the center of the print gets LOTS of exposure, the corners, edges, much less. Very uneven print. UGLY.
Of course, you could burn the edges like mad and probably not achieve a really graceful result; it won't be rational like the "falloff" - the effect of the cosine. This requires a small amount of edge burning (which most people wouldn't even notice) because the light source (here the lens) is farther away from the paper at the corners than it is in the center (that, too, means lost light but it is MUCH easier to deal with). Usually about 20% on each edge, giving twice that on the corners, is adequate for that. It won't change much, but your images will have a subliminal authority that would be missing if you don't do it.
I learned all this stuff the hard way in commercial custom labs with exposures that sometimes required hours. In one case, I thought I'd save time by printing wide open. I gave a 15 second main exposure and had to burn for two hours. Had I given the whole thing a 2 hour exposure, I'd hardly have had to burn at all. A very painful lesson, not to be forgotten.