One of the typical pop culture motifs surrounding the Merry Men stories is the concept of them poaching the game and being hunted by the Law (or at least, Wardens) for that.
This seems rather counter-intuitive to me: it's not like game wasn't plentiful; and prohibiting lower classes from hunting it only seems to have negative consequences all-around: the people are more hungry; and less satisfied; and you have to spend extra on enforcing the poaching laws.
If so, are there any meaningful reasons for why the King wouldn't just say "hey, anyone has permissions to hunt in Sherwood Forest!", which appears to be a win-win for everyone involved (the King gets better fed and thus more productive populace, less discontent and rebellion. The local authorities get to stop spending resources running down poachers). And since the King's the one decreeing this out of the largesse of his heart and care for his subjects, there's no loss of face for the monarch.