Grass is like most things, it grows in a 'S' curve. If you mow it too tight, it takes a long time to come back as there is not enough leaf to take in energy from the sun. If you let it go too far, it's growth slows. So you want to keep it in the middle somewhere. I always feel most grass is grazed way too tight. About 4cm is a good basis I would think.
Aside from worms, you should also consider the effect that animals have on beneficial plants in the sward. There is much research on the benefits of plantain to sheep and they will seek it out. If you keep the sheep in the same plot, they will just keep snipping off the new plantain leaves and eventually, this kind of treatment will kill most plants. A couple months of rest will allow those plants to establish themselves again without being hammered.
Our farm has been let to 2 graziers for many years by my father. One moves his sheep from field to field over 20 acres. The other leaves the gates open and they graze back and forth as they wish. It's interesting to compare the pastures after 12 or so years of this as the pastures that are given rest are far more diverse than the others which are going to thistles and nettles.