There's a reason J. Edgar Hoover held power for 48 years.
Kennedy wanted to "break the CIA into a thousand pieces"[1] and had a trusted brother as Attorney General to help with the task. And we learn 70 years later that Oswald was a CIA asset[2]. It's enough for even a President to sit up and take notice.
1: https://nsarchive.gwu.edu/sites/default/files/2025-03/2025-0...
2: https://www.newsweek.com/new-documents-shed-light-cias-conne...