I'm not sure why you persist in arguing, since you cannot prove that he would have used it throughout his theoretical X3 nor that it would have made the final cut.
What we saw of the firebird in X2 was a few final seconds with it underwater. If we had it around Jean every time she used her powers in X3, that would be far more expensive. So, as i said, budget could have become a concern.
Furthermore, the budget in X2 was also an issue and led to the removal of Sentinels, the removal of a massive Phoenix firebird blast that destroyed the Sentinels in their hangar at Alkali Lake, the removal of Archangel, the removal of Gambit, the removal of the Danger Room and several other things.
And, also, X3 was made more expensive partly because the main cast had signed two-film contracts (covering X1 and X2) and had to renegotiate for the third movie.
Additionally, judging from the astronomical costs of Superman Returns, especially in comparison with X3, I'm not convinced Singer's X3 would have been cheaper.
Finally, I just want to point something out here, just to make it quite clear to you because I can detect you are being somewhat adversarial as though you see me on the other side of some imaginary fence and just want to argue. I'm not anti-Singer, nor am i anti-firebird, and I would be quite interested to see what had happened (and what X3 we would have got) if he had chosen to stay on and do X3. But the fact remains that for various reasons, that didn't happen and nothing will change it.