I'm afraid this would not work. Consider LotSB. Or Arrival. Or any of the DLC in ME2. When you get to ME3 the writers have to take into account that many people may a) not have owned ME2 at all, or

if they did they did not have these DLC. Then what happens to your scripts? They become even more complicated trying to keep track of all the variables. It also means later stories become less understandable because players may not have the background material that is implicitly included in the story they are currently playing because it references DLC material they never owned.
Let me give an example of that last point. When TIM say "I've been fighting the reapers longer than you can imagine," my only thought was, "No, sorry. I have know about the Reapers longer than you have." Then I found out there is some comic or novel, or something, where it turns out TIM was exposed to some reaper tech around the time of the first contact war. All the sudden his statement might have made sense. But it didn't make any sense until I learned about that content. Certainly nothing in ME3 explained how TIM's statement could possibly be true.