“In that sense, the closed loop system has become open loop.”
Maybe. But cows don’t have anything to do with it. Neither do rain forests.
Every mature ecosystem is carbon stable.
There are only two parts of the ecosystem that sequester carbon - oceanic algae, as it drops to the depths, and humans, as they cut down trees and put into places where it won’t rot. (I.e., building homes and landfills).
You better watch out for termites because they have a microbe in their gut that converts wood into sugar/starch.
Most of the coal on earth was created during the carboniferous period, long before there were humans.
There are different theories. The lignin theory is that early plants were all small because their branches weren't strong enough to grow large. But they evolved and developed lignin which is strong and flexible, which allowed plant to grow to great size.
And the microbes and other critters that decayed the wood didn't know how to break down lignin. So all these trees growing wouldn't decompose and it took a million years for the microbes to evolve so that they could breakdown the lignin. Trees would grow and fall over and over and over and the accumulated weight and getting covered by earth would compress them into peat, lignite, bitimunous, anthracite, depending on time, temperature, and pressure.
Coal can also be made from peat growing in bogs. The coal in the Powder River basin in Wyoming is peat bog coal.