[Legolas]

In the end, Frodo neglected his mission and effectively died...he accomplishes little after his rescue by Gandalf and the eagles aside from recording his story and leaving his friends.

I do not think that it would've been wise to kill Frodo with Shelob. As well as bypassing the Cirith Ungol scene, it would defeated all the building tension between the triangle of Frodo, Sam, and Gollum with the Ring looming overhead. I don't agree with the contention that Sam vs. Gollum alone would've been trickier...it would've been less complex and more physical action as opposed to psychological struggle. The Ring's part would've been ignored with a simple Sam vs. Gollum, untainted vs. tainted struggle.

Frodo's death would've likely pushed Sam past his boiling point - Sam would've killed Gollum and suffered through to the end, nobly tossing the Ring into the fire. Sounds boring to me. Also absent would be the mark the Ring left on Frodo that held him back from enjoying the rest of his life, despite having 'saved the day' (however reluctantly).

In your hypothetical situation, having Sam, Merry, and Pippin return to Rivendell to inform Bilbo of his nephew's death would've been too negative a scene since Frodo would not have seen his goal to completion. A situation in which Frodo and Sam were both lost in the lava of Mount Doom after the Ring's destruction would've been more palatable to both readers and Bilbo.