In general, the more growth that can be left, the better. New growth in fall helps prime these plants for rapid growth the next spring. In some respects, it may seem wasteful to leave so much grass behind. However, this ungrazed forage serves a valuable benefit. The ungrazed grass moderates the micro-environment in which the plants grow.
Temperatures are cooler in summer and warmer in winter.
Evaporation and wind speeds are reduced. Snow can be trapped. The ungrazed forage allows more rainfall to infiltrate into the soil rather than running off. In essence, the rainfall is more effective. This ungrazed forage also comes in handy the next spring if rain is slow in coming.