You will never get me to believe that you can have a system of measurement without a UNIT of measurement.
Have you ever, by chance, studied the way the actual (SI) units of measurement are defined? The second and the kilogram, which are both arbitrarily defined*, are
used to derive 6 out of the 7 standard units. Only one other unit (the Kelvin) is not defined in terms of these two. That's a
good thing. It means that, even though the base units are arbitrary, all of the measures are
consistent with each other.
We have this system of measurement, now, only because of hundreds of years of study during which scientists catalogued and refined the fundamental laws of nature that govern the interrelationships between different physical phenomena. The only reason we haven't unified the second and kilogram, for instance, is because no one has yet to unify gravity and relativity. Many physical units are named after those who discovered these fundamental laws, such as the Newton (which defines force in terms of mass, distance and time) or the Ampere (which defines current in terms of mass, distance, and time). Yet, still, the base units from which the others are derived, are arbitrary.
So, since you are fundamentally opposed to a similar kind of arbitrary definition of economic "units", have you done the same for, say, gold? Do you know the physical law that determines the economic conversion between gold and steel, for instance? (This would have been nice for Greenspan to have known.) You haven't found it? Better get to work, then. Once you discover this fundamental objective ratio of value, I'm sure it will be named after you, and then you can feel free to lecture us on the fundamental superiority of objective units of measure. Until then, take a look at this arbitrarily-defined kilogram, and perhaps try to gain a little perspective.
*And here's the definition of the second. Does it sound anything like the definition of a Bitcoin to you? (It should.)
the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.[1]
If that seems a little too precise, go back and look at a previous definition:
Between AD 1000 (when al-Biruni used seconds) and 1960 the second was defined as 1/86,400 of a mean solar day