A few ideas that I personally would like to see in TE, to reinforce the immersion of the career mode:
1- An area in the character sheet to add a picture of the player (obviously, meant to be added manually or by mod, for rights reasons).
2 - In the career mode, interactions with the agent, the coach, the media, like what you find in a concurrent game. In TE, it could be done relatively easily with text (with the portrait from my first point), like a visual novel. It's a bit like the request for cinematics that has already been made (Sekir on page 13).
The interactions could have an impact on sponsor contracts and a popularity rating.
Obviously, this could be optional.
3- the possibility (again, from concurrent game), to simulate a part of the match (eg. a set), allowing to play matches faster while keeping the 3 or 5 sets format (request close to the one of knich on page 18).