This question goes further than the argument that Edward Kenway is important because he's Haythem's father and Connor's grandfather. Edward's actions in the West Indies and those years after those events, in my opinion, are some of the most important actions and events in the entire series due to what resulted from them.
As an example, if Edward were to have never left Wales for the West Indies many characters important to the "future" games would not have made contact with the Assassins. Adewale is one of these, who is important for the growth of both the Haitian and Colonial Brotherhoods. Not to mention his acquisition of the Precursor Box in Freedom Cry set the stage for the earthquake in Haiti, which would lead to Shay's conflict in Rogue.
Would love to hear comments and criticisms on this.