Well, more people will read the books for sure.
And the problem with cutting old Sharku miserable end's: giving the completely wrong feeling that LOTR finish with a happy end. It wasn't, isn't and won't ever be for me. Evil is defeated but the price is that the greater power of good are forced to walk away. If you stop LOTR at just the end of the Aragorn+Arwen celebration then it could be summarized as pre classic D&D advantures. It has more classical Greeks root (Oedipus ... especially frodo->aragorn & pippin->denethor & merry->theoden) roots than anything else. So it has to end badly for the main character(s) :-)