Why not? It seems to work for you.
And yes I have played all of the FF series and beat them all (without cheats) and gotten all side quests on all of them.
However the question was how to kill one, and in those series the Pheonix did not play an active role, he revived your party member(s) yes, BUT, he did not fight, he took a passive approach to victory. Therefore if he did not fight then what's the use of wondering how to kill that pheonix in question?

Maybe tonight we'll fly so far away... We'll be lost before the dawn...