Soken's argument is that :
- People want the second part of Sephirot to be on the mount;
- But then, people will miss the Warring Triad song;

Solution is easy:
- Put the Sephirot music on the Warring Lanner
- Put the Warring Triad song on the Firebird

That way, you have all the songs, plus the Firebird is currently using the default music, it would improve the reward experience of getting that mount. Finally, the warring triad song is used in Sephirot, in Sophia and in Zurvan. All three fights in which you need the mount to get access to the Firebird.

BONUS:
Some other mounts should have specific music. Like the Gil Turtle could be playing the Gold Saucer music. The Falcon mount could be playing the "Searching for Friends" (although I admit that this song doesn't exist in game at the moment). The Beast Tribe mounts could play songs that play in their beast tribe encampment, etc.