In your thought experiment the number of extant cows is a variable determined by human behavior as opposed to inherent regulation. There might be historical population numbers from specific regions where carbon was in equilibrium but that's certainly not where we're at today nor is it a goal of ours.
I think we're only able see some carbon sources as "outside the cycle" due to our infinitesimal lifespans.
I think we're only able see some carbon sources as "outside the cycle" due to our infinitesimal lifespans.