I'm not capable of following the mathematical argument, but I'll take your word. As for practical measurement... Colman mentions unemployment, but let's go straight to employment, annual hours worked, where there are different measurement tools, concepts, and calculations, making international comparisons impossible (says OECD), and don't let's go on to output, productivity...

Possibly practical decisions can be made within one country, much like a businessman who doesn't understand his balance sheet, or has reason to know it's bs anyway, can still have a canny sense of how to run his business. But it's seat-of-pants flying... And may end in a nosedive.

The pretension to accurate drawing of a universal picture seems to have taken a knock with the World Bank's China PPP announcement. But if you're right and it's Aristotelian physics, 40% or 4% yardstick error, what does it matter?