Let's look at Aragorn for a good example. Before hooking up with Frodo and the fellowship, he has a mountain's worth of back story; a broken sword, a king in exile, an elven lover, etc, etc. How cool is Aragorn's story if he is killed by wolves after leaving Rivendell with the fellowship? Aragorn's back story is huge and having him randomly killed by the equivalent of wandering monsters is very anti-climatic. A player who brings Aragorn to the grim and gritty game is going to be very disappointed as the time spent in building the character may be wasted before the first session ends. On the flip side, Aragorn is perfect for the Lord of the Rings. He has lots of interesting hooks for the DM to use and his story is a driving factor in the plot of the game.
I think you have things a little backward. The issue isnt necessarily that Aragorn has a lot of backstory. Backstory is filler, its not very useful and if a character with lots of backstory dies so what, it hasn't actually affected the game very much. The frustrated novel writer player can create another character with a new backstory and be very happy.
The issue is that Aragorn has a lot of "story now", that is, issues in the character which demand to be addressed in play. How will his love affair with the princess turn out, will he dump her for the affections of a pretty horsemaid, will he ever return to the white city and claim his throne, can he withstand the corruption of Sauron or desire for the ring.
Killing Aragorn doesnt remove a bunch of backstory, it takes away a huge chunk of exciting and interesting drama and opportunities within the game. You could bring a new character in but he wont be as tied to the events that you already have running and will, almost inevitably, be a much damper squib.