Lawrence Lessig gives many good reasons for remixing in his book Remix: Making Art and Commerce Thrive in the Hybrid Economy which I have read and enjoyed. Writing fan-fiction and crossovers, whether in fiction or in non-fiction (see some of my crossover essays) is the writing equivalent of what he describes being primarily done with music and videos.

Our aversion towards fan fiction and an insistence on "originality" is mostly a 20th century fad, that is slowly (for some values of "slowly") diminishing.

Anyway, the various fiction franchises and idea systems that influenced me are a large part of me, and I cannot throw them away when writing my own works. I don’t have a lot of control of the ideas I come up with, but I know I must materialise them eventually.