They can still tell the story of the assassins vs the templars through the generations without some future narrative going on at the same time. I mean, ACIV practically did away with it as it is and made the future stuff an elaborate joke about game design with barely a connection to the "main" narrative. The big thing connecting the future story before was Desmond, and well, that's not really a factor anymore.
The core concept of the AC franchise isn't the act of going into memories through the Animus, that is merely the excuse used to explore the actual core concept of going to different eras of history and locations around the globe that don't usually get seen in games. To make games in the same series take place during the crusades in the middle east, the renaissance, the American Revolution, the Caribbean during pirate times, etc.