More to the point, this seems like a misreading of GP's comment. Wyre specifically says that they don't want to impose taxes, that they want to very slowly cut or redirect subsidies instead. So I guess a followup question is, is the government currently giving you money to let deer fart in your pasture? Because if not, you'll also probably be OK.
The number of cows in the world is immaterial to the stated concerns though, since it's not the number of cows that determines the amount of methane produced — it's the amount of biomass they are digesting. So if the number of cows is reduced but the amount of biomass consumed stays the same (being digested by deer, rotting in the field, etc.) there's no net impact to the methane produced.
A) different animals produce different amounts of methane. Even among cattle animals, there are efforts to decrease the amount of methane they produce[0]. And nobody is laughing at those scientists and saying, "this is silly, they're still going to eat the same amount of feed so this can't possibly work." It's not just what's digested, it's how it gets digested.
B) if we have fewer cows, we don't need to replace them with the same number of another animal -- the point is we could have fewer grazing animals entirely, because our agricultural industry does not exist in order to feed wolves. We don't need to increase the number of deer by however many thousand times to sustain that ecosystem.
That was kind of my point. If you are planning on keeping the total number of grazing animals constant by massively scaling up the amount of deer, then maybe we have a problem. But why are you doing that?
If you're proposing that the current volume of cows/biomass consumption we have is a natural constant, and that other animals would just move in and take their place -- that's just not the case, we are artificially boosting the number of edible animals in the world, and by extension, we are also artificially boosting the amount of feed produced and consumed. Before the agriculture industry scaled up, we didn't have the volume of corn we currently produce lying around and being mass-consumed by deer. We started producing a lot more corn/grain and then breeding a lot more herding animals that we then fed it to.
[0]: https://www.cbc.ca/news/technology/livestock-ghg-emissions-s...
By the way, deer are not a meaningful contributor to atmospheric greenhouse gas levels.
Suppose you set up a polluting machine that solely emitted carbon, perhaps for art. That goal may be reasonable, but by engaging in it you’re hurting others. A carbon tax makes them whole (by either paying for carbon capture or by direct compensation) and disincentives you from doing it in the first place. If instead it was a naturally occurring polluting machine (a herd of deer, say) then we’d either want to remove it or do something to counteract it, and that cost is paid by everyone. In this case, we’d probably choose to plant trees, rather than killing the deer. (Although the deer population in North America is out of control, so perhaps killing them might be the right choice.)