If Marilyn Monroe Was Murdered ...

... and I repeat if - I have a new suspect with ample motive, who to the best of my knowledge has never previously been suggested. We have heard about her friends, politicos, gangsters, big names and mafiosi as likely perpetrators but I have a question:
Why was Joe Kennedy never put forward? - He would have arranged anything to protect the reputations of his sons. (He actually combined a number of the categories above.)