It is no coincidence that some of the greatest diversity of wildlife is in hunted country. Destroy the link with hunting and this important benefit will suffer.
The banning of coursing or hunting hares will actually make their lives harder and their deaths more frequent and unpleasant, hunting and coursing ahve their own rules and the people who do it (legally) do care for and respect their quarry, poachers dont and it is poachers who will continye after a ban