I watched it many times and didn't get it. Then I put myself in Kay's shoes. Kay appealed to Michael particularly because she was not Italian, not part of the "family", not part of the business. He harbored illusions of turning the business completely legitimate for a long time, well after he married Kay. I think marrying someone who would help discourage him, even just by her presence, from following in his father's mold, was very appealing to him. I imagine that the murder of Apollonia actually made Michael more insistent that he marry Kay and at least try to escape from the cycle of retribution.
It succeeds not only in pulling off the use of a classical/formal/mannered film language correctly and remarkably; that language is used to emotionally evoke a grand archetypal American narrative, Operatic and Tragic, built around an immigrant family, and charting its rise, corruption, and fall in ways that comment on a vast array of subjects that relate to the American condition: Marriage, Politics, Poverty, Crime, Innocence Lost, Violence, Loyalty, Betrayal, etc. etc.