You do bring up an interesting point, but I think you are missing some vital piece of information; I cannot recall if it is there. Maybe you should replay the game, if you didn't abhor it, to find out the answer. Or maybe I should - I really liked the game. I think that it wasn't feasible or plausible to destroy that machine. Anyhuma, Ultimecia's Castle is one of my favourite final dungeon in the Final Fantasy series, actually correction - it is my favourite final dungeon.
Well the party could have tracked down her ancestory and kill a few of them off which would prevent her from being born. That is all theory because if time is seperate, all the party would have done is create an alternate universe without Ultimecia, but Ultimecia would still be threatening their [the party's] universe still.
After some quick research, Dr. Odine from the future created the Junction Machine Ellone, meaning that the party couldn't destroy the machine. Again, they could kill off Dr. Odine but that may just create an alternate universe and not solve any of their problems - with time involved, nothing is knowable.
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