We'd need to chew on rough things to keep our teeth even and free of hooks, ramps and blades - as do horses and many other herbivores. If the grass or hand-feeds are too soft, these animals need to see a dentist every year, otherwise the inner linings of their cheeks get lacerated and infected.
It would be fine I guess. I'm thinking of things that do grow back when we lose them....hair, skin, nails, and the one that grows back at fast speeds and can come back bigger, fat. ;)