I do prefer the approach of last-gen MyCareer which included the Combine, Summer League, D-League, etc. and focused on the path to the league. It was experience driven without the need for cinematics, and this left narrative to the imagination of the player.
Cinematics within the mode could have a universal appeal IMO as sequences, cutscenes and events that are centered around the life and experiences of a basketball player. But when the story starts delving into particulars, such as family, environment, upbringing etc., it inherently becomes exclusive on some level(unless there is a broad level of customization there)... so I do agree that the current approach presents an issue.
From what I can see, 'Livin Da Life' has specific elements within its story-line and for all intents and purposes, we are 'Frequency Vibrations' in this game... so for me I wasn't expecting an immersive experience from the standpoint of the story this year. I think at least that once the story is no longer central to the mode(by the second season I've heard), a greater sense of immersion may be available to all players.