I doubt whether we could sustain the world's population on meat – at least not meat which I would like to eat. It certainly bears reasoning that any party which demands compliance would also prefer its subjects to be fed on vegetables.
At some point I think either lab-grown meat, or sufficiently realistic synthetic "meat" will become cheaper to produce than the real thing, and real meat that has come from an actual animal will come to be seen as more of a luxury item. There are other factors that can accelerate this trend, health concerns, climate impact, etc, but price to the consumer will be the fundamental driver. Would you pay $2 for a fake or lab-grown steak that is 99% realistic, or $20 for the actual thing?