Depends on how one would define "failure". A martyr's death often accomplishes nothing in the moment yet lays the groundwork for successful revolutions and societal change decades down the line.
Since we're going whole spoiler mode now the metaphor/allegory suffers from a purely materialistic understanding of the world. To one who can or will only allow themselves to view the world in a materialistic lense your point makes sense.
I am, however, not a trained theologian and thus risk screwing up in a big way and thus promulgating heresy if I try to fully answer why saving the innocent child doesn't actually correlate to Jesus upon the Cross. However, there is one point I can make that I know isn't wrong. See, our lord didn't die upon the cross to "allow" us to sin. Rather, it was God fulfilling his covenant with us. A covenant he, in a most idiotic of deals as any mortal human would understand it, assumed full and total responsibility for. We would get all the benefits no matter if we fulfilled our end or not. If we broke it, than we'd still get the benefits and God would suffer in a most severe way. Look up what a "covenant" meant to people of the ancient world and you'll understand really hard and fast why God taking full and sole responsibility (at least in regard to the consequences) for its breaking was such a big deal.
However, that isn't to say we're all off the hook because of Christ. No. Now we're all on the hook to do as Christ did. His sacrifice was a perfect example of Charity. Charity, properly understood, isn't giving money to poor kids in Africa. It's to wish the best for others no matter what out of our love for God. To love him as he loved us.
He has fulfilled his end of that rather one-sided bargain as an example for us all. He showed us all how much he loved us at Calvary. He is mercy and love, but he is also justice. Justice demanded Calvary, and it now likewise binds us to follow his example.
The Innocent Child at the heart of Omelas is, like many things and arguments that attempt to use Christian logic and theology against the faithful, a demonic subversion/inversion of the truth. They in actuality suffered needlessly. Those who walk away get and understand that and their revulsion about that fact is what causes them to walk away but, like I said, they wouldn't just walk away if we want to actually make them human. Indeed, it would be God's will to build the Mechs and stomp this nicer and somewhat more sympathetic equivalent of Sodom and Gomorrah flat as a pancake as you used all the other weapon systems because unlike some puritain's understanding of things it's actually OK to have fun while you do the right thing!
I mean, if you got a 140mm main gun, flamethrowers, missile packs no doubt, rapid fire recoilless rifle systems, 50-cals, and whatever else you tacked on just for giggles why not use em'?
Now, for a recommendation of a story/series that gets this kind of thing so right it hurts. If you haven't heard of Yasuhiro Nightow and his Magnum Opus "Trigun" I'd give it a gander with this little intellectual primer. It's a deeply Catholic work on the same level Lord of the Rings was. Like the latter you don't have to be familiar with that tradition to enjoy it but if you are holy friggin' hell do you see it hard. I don't wanna spoil the scene I'm thinking of but you'll know it when you see it...
Vash would've tried to save the child. He'd not relish having to murder the inhabitants of Omelas to do so but if it came down to it he'd fire his gun with the full intent to kill if need be. Wouldn't like it, would wish there was another way and hell probably pray the bullets didn't hit anything vital but if that's what it took to save the kid than that's what it'd take. Up to and including using the... well, that's another major spoiler but if you know you know and yeah that'd be on the table.