Update to the functionality as it stands today.  In order for someone to share a search the need to be a search admin, that is given out based on general security role.  And we can't assign it to the 'None' role as it's blanked out.  So we'd need to create a role fro everyone who would want to share a search.  I can't see why this wouldn't just be a feature given to everyone.  Also, perhaps there is a way to share a search with more than just the groups you belong to.  There could be more people that you want to see the search but you aren't in a group with.  less than global, more than just the group.