The thing is, immersion shouldn't get in the way of good game design, ever, or you're just asking for clunky systems. (1.0 with its 'rested exp' system trying to be immersive as an example...lol)
Also they kinda busted immersion for AST considering the cards no longer do the effects that they do in the lore (all cards give damage, where in the lore the Bole enhances defenses, etc), so they've shown they can violate it if it leads to more balanced gameplay. WAR also no longer uses its inner beast to protect others and enhance its defenses like in the lore, its just a straight damage move now.
I brought up the enkindles and deathflare because its just a simple exclusivity thing. You can't ever use enkindle bahamut without having first used and gone through Dreadwrym Trance. Thus Deathflare is just button bloat for the sake of it. I'd go one step further and say Dreadwrym Trance, Deathflare, Summon bahamut, enkindle bahamut, Firebird Trance & Enkindle Phoenix could all literally be the same button since you need to use the one ahead of it in order to reach the next. 6 skills that could literally all occupy the same space, and yet occupy 4x as many buttons than they need to.
If you want to go off immersion however, it makes sense on that front too. You start in Dreadwrym Trance, unleashing your aethertrail to use Deathflare, which then enhances your trance to allow you to summon bahamut, which in turn allows you to summon Phoenix. A natural progression of power. Since you also brought up fountain of fire & brand of purgatory, those two could also occupy the same button. brand of purgatory is stronger than Fountain of fire so there's no reason you're using Fountain of fire x2 in a row, so you could just make ruin 3 turn into fountain of fire, then have Brand of prugatory replace fountain of fire under hellish conduit instead of having to know where your outburst button is just to continue it. (Also since you can't even use Brand of Purgatory without using Fountain of fire first, its just clunky to put them on different moves.)
I won't comment on the last bit since that's just opinion based, but my opinion is that its just clunky. When I'm doing my rotation, I don't feel any special attachment or emotion to using some super skill, I see it as just part of the rotation and move on. the benefit here being that Confitteor on top of Req means I can move another ability to my first hotbar for a more relaxed and engaging flow of my rotation vs having to manage more hotbars than necessary due to uneeded button bloat.