Elsa's death helped on a much simpler movie level too
Cole, you'd very much appreciate the ending to my Indy 5 script.
Back to topic, I think Elsa's death added an extra dimension to Last Crusade that it greatly needed. In pure, simple, cinematic terms, it helped stage the scene and excite the audience.
Now, don't get me wrong, I love all four films, but I think Last Crusade is slightly overrated at times, mostly because so much of it is a retread of Raiders -- There's not as much originality in it. Same villains, same locales, same gags half the time.
But the leading lady dying was something no other Indy movie -- and few adventure movies in general -- can lay claim to. Elsa's death, for all its other filmisophical reasons, also gave us a whopping surprise which ratcheted up the drama of the scene. Imagine if she lived. The Grail would just be there in a ditch, and we'd have no reason to believe Indy couldn't get it. Moreover, when he couldn't, we think him a bigger idiot than someone trying to do what just got someone else killed.
Back to Elsa. Nobody expected her to die. I'm sure everyone seeing this movie the first time expected her to live because . . . leading ladies live. The thought that she'd die never entered our minds. But when she fell, suddenly you begin to worry about everyone. That Indy *might* fall himself is suddenly credible, believable, and we fear for him, even if he *is* the unkillable hero in a heroic adventure movie.
There are many layers going on at any time in a good movie, Last Crusade being no exception. And many on this thread have brought up great points, usually ones wiser and more subtle than mine here. So I'm just taking the surface reason, the moviemaking reason: Elsa's death was good because audiences like to think they *know* what's going to happen, and when they're surprised, it's good for the excitement factor (Henry Sr. being shot was good for this same reason, in addition to the additional subtle layers of redemption and such).