It’s an interesting question. It’s not only how local the farm is, it’s also the type of farming practices. Not every small farm is going to farm sustainably. However, most big farms today do not farm sustainably. Farming meat at the scale demanded by consumers today means lots of derforestation and soil erosion, which means more carbon in the atmosphere. Of course, there are ranchers out their who farm sustainably — but again, exceptions to the rule.
My guess is that this level of consumption can’t be sustained, environmentally. Buying from small farms would likely be more expensive, which would in turn lead to a decrease in consumption.
> However, most big farms today do not farm sustainably
Is this true in the West though? It's not like we have a lot more forest to destroy... Soil erosion is definitely an issue, but AFAIK it primarily applies to growing plants (with e.g. artificial, fossil-carbon-based, unsustainable fertilizers), not animals.
The problem here is that a huge amount of the plants grown go towards feeding animals. [1] That’s probably one explanation for why estimates regarding the carbon impact of meat production vary widely.
My guess is that this level of consumption can’t be sustained, environmentally. Buying from small farms would likely be more expensive, which would in turn lead to a decrease in consumption.