I think one of the most important prerogatives of a person with power is control over who can come into his presence and who can leave -- perhaps moreso the latter than even the former. Even unimportant people with few claims on their time tend to value privacy and seek to control and limit who they interact with, who comes into their presence. Important people tend to have secretaries and assistants who answer phones and emails and who make appointments for personal meetings when necessary. Time is valuable, so it's understandable that just about everyone attempts to control who they spend their time with.
Power over who can leave is almost unknown in America, and one implicit cornerstone of a free society is that a person generally has the liberty to leave wherever they are and to go somewhere else. The President may refuse to meet with me, but if we do meet and I tire of his company he cannot detain me on a whim. This sort of freedom is assumed in American culture, but historically a king has not only had the power to compel attendance, but also to dismiss or detain those in his presence.
The most visible modern American connection may be seen when children ask permission to leave the dinner table, although in my experience few families abide by this formality anymore. However, as I consider it, being required to ask permission to come and go could help a child understand his position in the family structure and lead to humility, and I think that when I have children I will enforce this practice.