Veganism will never save us there.
It's because meat tastes good. That's literally all there is to why we aren't all vegan. Humans will not voluntarily give up one of the nice things they currently have access to and enjoy. Nobody cares about delayed indirect consequences on a planetary scale. Our brains aren't wired to think that way, since it provides no instant gratification.
If someone came up with a novel way to create a meat-like material that actually tastes as good, without involving inefficient animal farming, it will be a much more successful approach at solving this problem.