So eliminating livestock would reduce emissions by 4%.
With that said, 4% is still low, but it doesn't account for all the GHG emissions needed to grow feed for livestock, nor does it account for other things like transportation of that feed, energy used in processing by the industrial sector, and so on.
You're conflating domestically produced GHG emissions with domestically consumed products' emissions. As a toy example, suppose we grew no animal products in the US and imported all our meat. Your method would conclude that switching to plant-based diets would have no effect on GHG emissions since livestock represents 0% any of our agricultural GHG emissions.
And process it, and transport it, and process and transport the meat after we've slaughtered the livestock.
Part of meat's increased GHG emissions are because their are so many more steps in bringing it to market and because it doesn't last as long.
Most plants are harvested, cleaned/processed, and transported to market. Livestock generally needs feed, which is harvested, cleaned/processed, and transported to the livestock, and after livestock is slaughtered, it needs to be cleaned/processed, and transported to market, and on top of that it tends to go bad faster.
https://cfpub.epa.gov/ghgdata/inventoryexplorer/#agriculture...
And ag is ~10% of US emissions
https://cfpub.epa.gov/ghgdata/inventoryexplorer/#allsectors/...
So eliminating livestock would reduce emissions by 4%.
With that said, 4% is still low, but it doesn't account for all the GHG emissions needed to grow feed for livestock, nor does it account for other things like transportation of that feed, energy used in processing by the industrial sector, and so on.