I don't think a full-on story with dialogue is necessary for FIFA's Career Mode (NBA 2K16 took it way too far IMO), but we need more than an e-mail inbox. A career is not compromised of a bunch of incremental stat boosts, but real-life decisions that carry weight and will ultimately determine your success.
One thing I enjoyed about earlier PES games is having an agent that shows up weekly and talks you through your career options. Are you unhappy with a team member? Should you ask for a raise? A transfer? A position change? What other teams are interested in you? Maybe you want to fire this guy and find a new agent? Little touches like this add a lot to the career aspect, making you feel less like an in-game character and more like a real footballer.