A perilous gesture the invitation. While the vampire seems to be the only variety left still upholding the practice, in the folklore of old is what a common trope that all denizens of the night and the wild, from the mischievous to the nefarious, could not simply barge into one's home despite their otherwise awesome powers. They had to be invited first.
These stories date back to a time when hospitality was king and when the ill treating of a guest was one of the most heinous acts a person could do. It is perhaps easy to imagine the point of the tales. To serve as gentle reminder that one must after all set some limits on one's courtesy. Some doors once opened are nigh impossible to close.