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Who said destroying the machine in the past? They could very well destroy it in the present, as well as the blue prints for it so it couldn't be rebuilt by someone else in the future. They can't change the past because it already happened, but they can very well change their future.
You're destroying the machine in Ultimecia's past. I mean, Ultimecia exists in the future clearly, so if Squall and Co can't change their past, neither can Ultimecia. Being unable to change the past in FF8 implies that all of time is set in stone.