Okay. If a given carton of eggs weighs 1201g, how much does 1/3 of that carton weigh? If the volume of the eggs in a dozen is 769ml, what is the volume of 1/3 of that carton?

Some eggs are smaller than others; some are more dense, etc. Yes, the "count" is maybe sort of interesting in some very specific contexts, but certainly not in any reductive physical context. It only works in an economic context because we have standards like what constitutes a "chicken egg large white grade AAA".