You say that "same page width/height ratio is maintained between the different page sizes" is the important thing, but it's the result of using that particular ratio that is important, when you take a page of 1/2 the area by cutting across the long dimension, the aspect ratio is maintained.
If you aren't worried about maintaining the aspect ratio for 1/2 pages, you can maintain any arbitrary aspect ratio as you scale up and down (but you don't get the 'easy' scaling to half or double areas).
That's where the imperial fluid analogy comes in, there is convenience derived from having it be base 2.
The fluid measurements analogy doesn't work though because volumes don't behave the same way as areas with fixed aspect ratios. Moreover, the reason why √2 is such a useful ratio is because it maintains the same aspect ratio when the sheet is doubled or halved. That's why his argument was nonsensical.
If you aren't worried about maintaining the aspect ratio for 1/2 pages, you can maintain any arbitrary aspect ratio as you scale up and down (but you don't get the 'easy' scaling to half or double areas).
That's where the imperial fluid analogy comes in, there is convenience derived from having it be base 2.