JFK's many paramours are very interesting in that one Judith Campbell-Exner was a courier and liaison between JFK and Chicago mob boss Sam Giancana. https://www.youtube.com/watch?v=tsX1QaITl3k&list=WL&index=35
Yes, organized crime leaders have sometimes had political influence throughout history in different nations. Political leaders use them to be able to carry out their dirty work, and in exchange the organized crime group gets some degree of protection from high up in the government, securing a lucrative monopoly on illicit dealings. Keeping black market activities illegal ensures continued corruption.