Ok. I'll be super explicit about this. The page measurements don't matter. What matters is that all the standard page sizes have exactly the same width:height ratio when halved or doubled to obtain the next size up and down. That's the magic property that the 1:sqrt(2) width:height ratio used in the ISO/DIN page sizes gives you. The fact that an A0 sheet is defined as having an area of 1m² is a distraction. It's the width:height ratio that matters.
Your comparison to liquid measurements misses the point. It's irrelevant. Your statement that the US units are defined in terms of US units is irrelevant.
What is relevant is the preservation of the width:height ratio between pages sizes in the ISO/DIN paper size series.
"That's the magic property that the 1:sqrt(2) width:height ratio used in the ISO/DIN page sizes gives you."
Which is very similar to the "magic property" that you get when you have measuring units that are powers of two rather than factors of ten. So, no, I"m not "missing the point" at all.
That you think this is "irrelevant" indicates to me that you haven't done a lot of cooking.
Yes you are, because _this has nothing to do with factors of ten vs factors of two_. This is nothing to do with US customary units vs metric. _The units are irrelevant._ That's what you're not getting. What is relevant is that the same page width/height ratio is maintained between the different page sizes.
Your comparison to liquid measurements misses the point. It's irrelevant. Your statement that the US units are defined in terms of US units is irrelevant.
What is relevant is the preservation of the width:height ratio between pages sizes in the ISO/DIN paper size series.