The reason that the mirror is left out of most games while in chase mode is simple.
Performance. When you are in your car, the game is not drawing your whole car's body. Opponent cars are generally drawn at a lower Level of Detail...so they aren't as heavy. However, when you are in chase mode, YOUR car is drawn at MAX LOD ... with reflections and such. All of this extra power needed for that means that drawing the mirror is to heavy. Remember, the mirror is essentially just an extra "camera" rendering the whole scene behind you...
That said... lfs runs on my machine at 100fps all the time, and though my machine is relatively new, its by no means a powerhouse. There is enough power left for an extra mirror (i never drive chase, so that number is in-car)
For everyone saying "its not realistic" ... think of it this way. Whether you like the view or not, people will be using it. People who are racing WITH YOU. As long as that view is there, it should have a mirror. I think its a dumb view, but if I'm racing people who are using it, I want them to be able to see me lapping them. (lord knows they aren't up front if they need chase to drive)
The mirror is more for the people the are racing with than it is for them.
However, in a perfect world, that view wouldn't exist. You drive from the seat or you don't drive at all.