Why save them?

[Boromir88]

Besides what has been said I also think that Frodo was sacrificed. He just wasn't sacrificed in the sense that he actually physically died. But, I would say he was emotionally scarred and altered so much, that after the ring's destruction that Frodo alread committed the 'ultimate noble sacrifice.'

Once we get to Mount Doom, Frodo is no longer himself. He has lost control and his own 'mind' to the Ring:

”No taste of food, no feel of water, no sound of wind, no memory of tree or grass or flower, no image of moon or star are left to me. I am naked in the dark, Sam, and there is no veil between me and the wheel of fire. I begin to see it even with my waking eyes, and all else fades.”~Mount Doom

Frodo can remember nothing else, he sees nothing else, he is nothing and all that's there is the Ring...'the wheel of fire.'

Tolkien talks a little bit about memory. With Gollum he was not completely beyond redemption, he was not completely ensnared by the Ring. We are told of this 'small corner of Gollum's mind' where he still has memory of his past life, before even coming across the Ring. And most importantly he still is able to remember his name...Smeagol. Most important, because contrast that with the Mouth of Sauron who we are told was unable to remember his past name. the Mouth was completely enthralled to Sauron's service, he lost all memory of his past life. Where Gollum still had this 'small corner' left.

Frodo is almost to this point of being completely enthralled to the Ring. He remembers nothing except the Ring. It is him, the ring and 'darkness.' By the time Frodo gets to Sammath Naur the Ring has complete and total control over him:

The suddenly as before under the eaves of the Emyn Muil, Sam saw these two rivals with other vision. A crouching shape, scarcely more than the shadow of a living thing, a creature now wholly ruined and defeated yet filled with a hideous lust and rage; and before it stood stern, untouchable now by pity, a figure robed in white, but at its breast it held a wheel of fire. Out of the fire there spoke a commanding voice.

"Begone and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom."~Mount Doom

The Ring now has complete control over Frodo. Frodo was now untouchable by Pity, the very quality we know that Frodo had...his pity and mercy for Gollum. Now Sam sees Frodo and sees him as 'untouchable by pity.' Then we go back to the wheel of fire, and it is the Ring that makes Frodo utter those words. Which seems strange...why would the Ring make Frodo say these words of 'begone and trouble me no more and cast yourself into the Ring of Doom.' It makes it seem like the Ring wants to be destroyed, so what purpose would the Ring have in making Frodo utter these words?

I think it was necessary for the Ring to get complete and total control over Frodo, and achieve it's goal, which was to get back to Sauron. We are told in this one moment that the Ring was at it's maximum point of influence, beyond anyone's will to resist:

I do not think that Frodo’s was a moral failure. At the last moment the pressure of the Ring would reach its maximum - impossible, I should have said, for any one to resist,...~Letter 246

So, in order for the Ring to achieve it goal, it needs to get Frodo into the Sammath Naur. But prior to this Frodo did not seem to have the strength to do it, and suddenly he conjures up enough strength (perhaps the Ring has some part to play in that again?) And in order to get total control over Frodo, where he would claim the Ring and the Nazgul would come to bring him back to Sauron, the Ring needs to get Frodo into the Sammath Naur, where it would be at it's 'maximum point of influence.' But, the Ring did not intend for providence and Eru to step in.

Anyway, what I'm intending to show with all this, is that Frodo had already been sacrificed...he did not need to 'die' in the sense of committing and ultimate sacrificed, because besides literally being dead, Frodo actually was dead in a sense. Letter 246 from the quote above goes on to say...

certainly after long possession, months of increasing torment, and when starved and exhausted. Frodo had done what he could and spent himself completely...

Frodo was physically and mentally drained. He had absolutely nothing left, to get the Ring to where providence could take over, it took everything out of him.

So, besides his life, Frodo had already sacrificed everything. He had sacrificed his comfortable life style in the shire, he had sacrificed every bit of mental and physical strength to get the Ring to where it needed to get to. And we see Frodo completely changed and scarred because of the Ring, so in many ways he was already dead and did sacrifice everything.