Grass bad for roaches?

Since I started using dried grass as part of their main staple, I noticed that they eat more and more, and more of them stay out to forage all the time. That makes me wonder whether dried grass and hay really doing them good, or they lack of something, and feel the need to eat more?

Recently, I have came across some reports suggested that small tortoise shouldn’t be fed grass, only hardwood or pine leaves since these contain less fibre and more protein, only large tortoise can effectively digest grass. Experiments shown that if fed only grass, some small tortoise would refuse to eat, and those keep eating would lose weight. Now I wonder whether this would apply to roaches. But than it is autumn now, and the temperature has dropped significantly in the last 2 weeks, this might have triggered some sort of internal clock so they started eating for the winter. Anyhow, I’ll decrease the amount of grass, and throw some hardwood leaves in the mix and see how it goes.