As far as I know, and correct me if I'm wrong, the only crime that guy committed was the terrorism. And, that terrorism didn't cross state lines. Why didn't the feds leave most of the investigating and all of the prosecuting to local authorities?
I'm hardly an expert in US law, but from what I understand there are two kinds of jurisdiction depending on the crime.
State crimes, which can only be prosecuted within that state and are the responsibility of either the local police force or the state police. That's what you're referencing. Actually, IIRC, the local police can request help from the federal government under special circumstances.
Federal crimes. These are crimes deemed bad enough that you can't hide from them just by crossing state lines. In these cases, all states agree that the federal government can intervene and their agencies can investigate. Going by the FBI's website, terrorism is one of those things.