I read the paper you linked. Are you seriously suggesting that if we stopped animal agriculture, wild animals would flood the countryside to the same extent as in the Kenya study? I don’t think that is broached by the study at all.
A single study will not tell you everything about everything. No, ruminants will not just magically appear in the landscape, we’re living in a causal universe, after all.
Suppose, for the sake of argument, that all ruminants indeed all grazers (also deer, giraffes, whatever) are extinct. Plants will flourish, not being eaten by them, then individual plants, or parts of them (falling leaves etc) will die as part of their normal life/reproduction cycle – and get eaten by fungi, bacteria, etc. Which will burp CO2 and probably other greenhouse gases.
The condition for nature to produce CO2 are simple: The presence of carbon in a form that can be oxidised, such as sugar and starches of which plants produce plenty, the presence of oxygen, and a critter, any critter, that can do it. Even if it’s just a single species, it’s going to eat the whole thing and release all the carbon back into the atmosphere. Consuming available energy to reproduce itself is literally what life is all about.
If there’s energy around that can be used, nature will use it. Have a look at the most biodiverse and productive ecosystem in the world, the Amazon rain forest: It has very poor soil because as soon as something dies, its remains are recycled by something else. Destroying the Amazon rain forest releases CO2, again planting stuff there re-captures it, but reconstituted forest doesn’t continue to sequester carbon indefinitely: Only until it has accumulated the amount of carbon that it needs to sustain itself, after that it’s going to be carbon-neutral.
You may be asking “but then how did all that oil and coal end up in the soil”: Highly specific circumstances: Plants were producing stuff that critters couldn’t eat. But we’re currently not in that situation and in fact critters seem to be ludicrously efficient at evolving to break up new compounds. PET was first synthesised 1941, in 2016 scientists found critters which can eat it – producing CO2 in the process, of course. That’s exactly what’s going to happen to all that herbivore-free land you envision. If we want to sequester carbon, care has to be taken that nature won’t dig it up again.
