Several posts seem to assume that the person at the head of a line has more authority to allow someone to cut to the head of the line than do all other people in the line.

What is the rationale for this assumption? Since cutting in at the head of the line has an exactly equal effect on all the members of the line, it would seem that asking the first person in line if you can cut in is no more polite, and makes no more sense, than asking the last person.