I don't think it's a spoiler to tell you that John Dillinger was shot to death by federal agents as he was leaving a Chicago movie theater. That was 1934. The trailer for Public Enemies shows a lot of cool Tommy-gun action, so it's a safe bet that besides Dillinger's death, someone's going to be trading lead. And of course that's going to be a big part of the movie's fun.
Here's why Kansas City is important. FBI agents weren't actually allowed to carry guns or make arrests until the Kansas City Massacre in 1933 at Union Station. Beyond that, Agent Melvin Purvis - portrayed by Bale in the movie - went after gangster Pretty Boy Floyd because of Floyd's suspected involvement in the massacre.
There you go. No KC, no Union Station? No FBI agents, no guns, no thrilling cinematic gunfights. You're welcome, America.