That's true as far as it goes, and you'll note I didn't say the big lens was "brighter". There's way more to gauging the effectiveness of a scope than just looking at the exit pupil, and there are all sorts of optical and/or marketing terms like "relative brightness", "twilight factor" and "relative light efficiency" to cloud the issue. At my age my irises will never open up to 6 or 7 mm, probably not even 5, so on the surface a 4x20mm scope will give me all the light that's possible, looking at just the exit pupil.
But if you think that means it is just as effective as a 3-9x40mm scope in dim light at 9x, then try the two side by side and prepare for a shock. That 40mm objective has admitted far more light into the same exit pupil (actually, a slightly smaller exit pupil) and you will be able to resolve much more detail. It may not be technically "brighter" but it is definitely better.
The Europeans do a lot of shooting at night, in much darker conditions than we do. Using your logic, they would be just as well served by 4x28mm scopes (7mm exit pupil) as anything...but what they actually use is 8x56mm and 9x63mm jobs. Same exit pupil, but the larger image resolves much more detail.
Yep, this all assumes that everything else (i.e. lens quality and coatings) is equal...and of course it never is...but the simple fact is that a 3-9x40mm scope on maximum power, compared to an equally-well-made 1-4x20mm scope on maximum power...definitely lets you see more. I don't care what the scopes say on paper...I simply want to see more.
