Why save them?

[Inziladun]

I agree with the observation that Frodo's survival specifically lets the reader see the emotional and spiritual aftermath of his undertaking. Dying was what Frodo expected after the Ring was destroyed; his sense of contentment with that is evident.

'Well, this is the end, Sam Gamgee,' said a voice by his side. And there was Frodo, pale and worn, and yet himself again; and in his eyes there was peace now, neither strain of will, nor madness, nor any fear.

ROTK Mount Doom

As a survivor, Frodo must confront what he saw as his "failure" at Mount Doom: not resisting the Ring at the end. It does serve to make the story more poignant.

Sam lives to be the conduit of history to future Hobbits. Through his children, he passes on his account of the War, and hopefully gives them a new found appreciation of the cost of their long time prosperity and peace.