Yes, but meat-eaters eat all those things as well. I fully support the ideas behind your story, but you seem to be operating from a “Yes, but..” perspective, rather than “Yes, and” — so your title should really be “Vegetarian diets ALONE are not going to save the planet”. If I’m a vegetarian who also eats seasonally, and who also eats locally, and who also tries to avoid too much of the mass-produced grains, I’m content that I’m doing the best I can.
The UN has just put out a report cautioning that we need to globally cut meat and and dairy consumption to avoid the worst effects of climate change. To that, I say “Yes, and….”