I agree the effects of overgrazing riparian areas are terrible and should be halted at once. However their are some good points to be held for the limited use of these public lands for seasonal grazing.
The first positive point which comes to mind is the development of roads and or access points along the stream. This could be a combination of physical and or monetary gains provided by the livestock. Then the order of nature itself come to mind. If all livestock were to be removed where would bugs get there food and shelter. Are there enough users of the stream ready to provide all the funds to manage roads,invasive plants,possible invasive livestock or predatory animals?

Might it be that proactive management of the grazing land would better serve the needs of all the people and animals involved. I would suggest the use of watering stations built away from the stream in well suited locations for a start . After the positive effects of this possible riparian fencing could be introduced.

In my experience people are better managed if given some sort of choice along with guidance.