The Mishima Conglomerate (and with it a large slice of the world) is controlled by Heihachi, but he's not content with sitting on his laurels. . . He can't get enough of power or wealth and he's been sweet-talking the world's biggest cheeses to get more of both. Eddy has an influential heritage but it remains to be seen whether Heihachi sees him as a powerful ally now that his father is dead. Who knows, maybe the cartel Eddy is fighting to destroy is more useful to Heihachi?
In that case it would make more sense for Heihachi to dispose of Eddy. . .