Dairy-eating vegetarian here, but I disagree.
1) The vast majority of consumed meat comes from animals that have so closely co-evolved with humans that any pathogens that can plausibly jump from one to the other already has (with sometimes devastating effect). If we simply limited meat consumption to cows, pigs, and chicken, it'd satisfy most people and strictly limit the risk of novel zoonetic pathogens.
2) Those diseases you list in particular are mostly unconvincing: SARS and COVID likely come from bats via civets, MERS from bats via camels, Ebola from bats via primates. None of these species make up most meat consumption.
3) E. coli is the best example, but plenty of people do get it from lettuce and spinach. That said, E. coli is never going to shut down the world in a mass pandemic.