Why do anything? Why did we put a man on the moon? What direct benefits did we recieve from that? If you can think of any answers to that, then you know why you put linux on an XBox. Some of us have a need as humans to explore and to go beyond the boundries set infront of us and to break barriers we are confronted with and then some people just accept these things the way they are presented to them.
Besides that, I think they wanted to spite microsoft and thier closed source ways and also to prove the portability of the linux OS. They put linux on palm pilots and wrist watches, why not the PS2 and XBOX?