It takes considerably less labor to farm vegetables than to farm vegetables and feed those vegetables to animals and also take care of those animals. So vegetable prices may go up, but considerably less so when compared to meat.
Crop labor has also seen a lot more automation in general than meat labor over the last several decades. Some crop farms are almost entirely automated (and International Harvester and other brands think that Level 3 self-driving tech alone puts them on a path to nearly full automation in the next decade or so), though obviously things vary based on which crop.
On the other hand, slaughterhouses generally haven't seen any automation and other than size/scale mostly still resemble their counterparts from previous centuries.
Got a source for that? I've never been involved in commercial vegetable farming or large-scale cattle raising, but small-scale ranching is really not that labor intensive in my experience.
Scale seems to be exactly the problem. Industrial scale crop farming is highly automated. There aren't similar automations as you scale up cattle, and slaughterhouse work/butchering includes several skilled labor tasks with no similar skilled labor equivalents in vegetable farming.
