What effect would that have? Generally there isn't that much of a shortage of plant based food(recent Russian effects aside, which would likely effect any model we had) for so I'm not sure what having an excess of supply would do.

Environmentally, sure. But I'm not sure it would do anything for price or supply.

Now I'm just rambling obviously, but if we made all animals for food illegal today there would be a drop in price as farmers try to find new markets for the land. But given that they have the overhead to deal with, within a year or three most of the excess of farmers would likely close up shop(either by choice or by bankruptcy) since there isn't enough money to live anymore. The market would level out again, probably a little lower than before, but that might change as time passes since there aren't as many fields to average out bad seasons. Just my guess.