Rabbits are more work, the yield is lower, and even sheep farmers have problems selling the wool nowadays. You can't keep them as cramped as chickens, mechanising everything wouldn't be easy, and they do not eat everything. There simply is no incentive to scale rabbit farming up a lot. There is more profit with other animals.
Rabbit meat is very healthy, people who have problems with other meats often can still eat rabbit. It's very lean - and that might contribute to it not being popular, fat just tastes great. Also rabbits have the stigma of a poor peoples food, like, most would need to by chicken feed, but you can feed rabbits with forage gathered everywhere, for free.
When I was a kid rabbit was the meat on my grandparents sunday table, buying meat was a rare luxury thing. that changed when meat was produced on industrial scale, with all those helpful chamicals. Chickens were primarily kept for the eggs.
That's why it's important to keep those traditions alive, we might bitterly need it again, oil will run out, war is raging again just a few hundred km away, and a lot of what humanity is doing right now looks like a Ponzi scheme, some day of reckoning is due, maybe not during my lifetime, but we can't go ahaed like that forever.
I gather most forage with a basket and scythe, mowing along paths and places that aren't used by farmers, small spots and the banks of the brook. I also keep the grass low around small trees an a christmas tree plot. All stuff npoone else would use.
