It's a case of flavor that the current Lore already justifies to some extent. We are able to access Dreadwyrm Trance and later Demi-Bahamut because of the Calamity scattering Bahamut's Aether all over Eorzea. Phoenix was a Primal that was present during the Calamity, whose Aether was also scattered in a similar manner, though Coil goes into detail how exactly that all worked out. Ergo, since the two are linked, it follows that we have the potential to summon a Demi-Primal version of Phoenix. The Light-suffused Aether of the First just helped us pull that off, somehow, and we get -zero- relevant explanation on that part, but that's the gist. Also, notably, Firebird Trance does deal more damage than Dreadwyrm Trance. By 400 potency or so on single target. I think it's technically less on AoE, but basically the GCD bonus damage given to us from Fountain of Fire/Brand of Purgatory is worth roughly twice that of Deathflare initially and the falloff, while there, isn't a big deal compared to using Phoenix itself.
Paradoxically I did better on 5.0-5.1 Summoner iteration that had oGCD Egi Assaults because it did encourage you to spend them properly. Because they couldn't 'fit' anywhere past the opener you just dumped them as soon as you could in said opener then stockpiled them before you could use them for Bahamut. I actually kind of miss that aspect to Summoner, but it's the kind of thing I'm not married to. I agree the current iteration is better but if I was to improve on it I would make Ruin IV into a Bahamut-specific spell or split Ruin IV into a separate button again, but ideally I'd rework Further Ruin's interaction with Egi Assaults and replace it with another system that has more room to be expanded on. It's fine that they're mobility buttons, but it would be nice if they built towards a non-Trance payoff as well.