Perhaps the second Death Star was started a few years after the first one, and they rushed completion of it for the events in ROTJ. I would think that it would be dangerous to the Emperor to only have one Death Star. After all, IIRC, in the novel for Star Wars, the other officers of the Death Star actually start to try to get Tarkin to use the Death Star to take over the empire and blow away whatever planet the Emperor happens to be on at the time. But two Death Stars would have the effect of keeping both of them loyal.