Benno,
I've highlighted where your logic breaks down. Yes, you are right, the "average" amount of light will be different in the scenario you describe.
Your mistake is that, when photographing, we don't care about averaging the amount of light hitting the film surface. We care about getting the proper amount of light for each point of the film surface.
Think of it this way: with the frame filled by your wall of light, every square mm on the film surface gets just the right amount of light to expose the wall correctly.
With the 90mm lens, not every square mm gets this much exposure, but every sq. mm of the image of the wall of light does. Yes, if you add up the total light hitting the film in the two exposures, the total amount will be different. But, the exposure for the wall is the same because the intensity of light for the area of the image of the wall is the same. Clear?
For your sky exposure, the light balancing mechanism is different. It's the aperture: The 300mm lens sees less light total than the 90mm due to the of the angle of view if and only if the aperture the light is passing through is the same physical size. At f/8 for both lenses, the aperture is a different size. The f/8 aperture on the 300mm lens is larger (more "light efficient") and lets in more light than the smaller aperture on the 90mm lens set at f/8 (which is less efficient and lets in less light). Voilà, the amount of light ends up being the same and the exposure is the same.
Your conclusions in the paragraphs about the two f/2 lenses are simply wrong. The illumination is the same for both lenses, because at f/2, the apertures for the two lenses are different sizes, which balances the difference in the amount of light gathered by the different angles of view, evening them out. "Speed is intensity X area" is wrong. Intensity x area = total light for light projected through lenses if and only if the aperture the light is passing through is the same physical size. You're effectively leaving the aperture size and the whole idea of f-numbers out of your thinking here.
Once you get your head around this, you'll kick yourself
Best,
Doremus
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