I fail to see anything in the least irresponsible about grazing an animal on public or otherwise ungrazed land
as I understand it there is no "public" land. It is all owned by somebody. Common Land has commoners rights accrued by various means, usually ancient.
Malvern Link Common is owned by the Malvern Conservators and commoners were granted rights in a re-shuffle in the 60's and when I was looking for a house in the area one house adjacent had grazing rights, others might have been a mile away but kept sheep.
The fact that you can walk across it is because of the duties of the conservators. In extremis they can evict anyone or their animal if deemed inappropriate.
I used to post adverts for the Malvern Fringe, strictly "by arrangement" on their land, because the local highways did not allow on their street furniture.