SE Editor-in-Chief here. We include <i> within <cite> because 1) reading systems often have different default CSS which may not even recognize <cite> and 2) <cite> often contains both a title and an author, and in those cases we want only one or the other to be italicized. SE's default CSS for epigraphs (probably the most common place where <cite> is found) is to give <cite> small caps, italicize the title if there is one, but don't italicize the author.
I believe our use of <cite> predates the modern definition of its use, and in any case it's so infrequently found in a web context that I don't think there's much agreement about how it should be used anyway. (For example MDN says the work title must be in <cite>, but at SE we often only include an author name, like <cite>--Shakespeare</cite>.)
Interesting, the permissible content in <cite> is mentioned as an example of conflict between the HTML standard as maintained by the W3C and that maintained by WHATWG [0] (W3C allows title and/or author, WHATWG title only). Since WHATWG has been the sole maintainer for a few years, I guess their definition "won."
I believe our use of <cite> predates the modern definition of its use, and in any case it's so infrequently found in a web context that I don't think there's much agreement about how it should be used anyway. (For example MDN says the work title must be in <cite>, but at SE we often only include an author name, like <cite>--Shakespeare</cite>.)