The real question is (for some reason not framed this way): how many ruminants us humans want to keep around and where? If less than now how fast we need to kill those animals?
Tomorrow we could have 100% of grassland completely devoid of ruminants and other grazing animals, wild or not.
What will really happen to ecosystems and climate if we do this? Do we have a previous point in history where that was the case? Are our models good enough to say it will be 100% positive as we expect?
And I you looks at methane emissions globally ruminants are far from the leading emitters, why not go more intensely after other sources incluing the fossil fuel industry (leaks & all) that are fully man made, non renewable and useless, rather than trying to convince India people to slaughter all their sacred cows instantly?
Wetlands are a large source of methane emissions, should we dry those lands? Same question about ecosystems and full climate impact.
I understand vegan use this as a talking point, but when you look at the big picture there seem to be more reasonable choices and compromises based on data than ruminant extermination.