The actual circulating money supply is also unknowable because you don't know if people are holding onto cash or checking account deposits for buying things in the short term or as savings for the long term. Both look identical but one of them circulates more than once per year while the latter circulates less than once per year.
It is not like we are sending a dollar bill through the economy and counting how many times it changes hands to estimate the money velocity.
If you could neatly split up the money supply into "medium of exchange" and "store of value". You could actually estimate inflation based on that equation.
