Good argument and I might be okay with it if it meant we'd get more unique buttons and job mechanics, but not sure I'll enjoy this as much in practice as I'd think right now.
The immersion aspect will still be violated and it's a line which hasn't been crossed yet, and maybe devs want to keep it this way out of having a principle and logic in place. I don't know what Geirskogul is, but looking it up I'm assuming it's like SMN Fountain of Fire and Brand of Purgatory from the Fire Bird trance. How I interpret that, is that this stance you go into transforms some of your current abilities into a more powerful one which makes sense from an immersion perspective, it's the same ability and does the same thing essentially but it's a more powerful version, due to the stance you're in.
Enkindle isn't like that since it's a seperate action that doesn't have anything to do with the summoning button, it's giving a command for an attack which doesn't summon it, while the alternating between Phoenix summon and Bahamut summon does make sense since you're doing the same thing for both actions but just a different version.
Again, I think devs consider this immersion principle and haven't been willing to violate it so far (maybe to avoid slippery slope?). It's easy to neglect immersion and having a sort of logic to your abilities when you still have it, but I think violating this would for some make the rotation feel less satisfying and less immersive than they'd think it would beforehand. It may also get more confusing if you're changing too many buttons into dual action and dual purpose. Some perhaps also value there being set "principles" instead of inconsistent change in structure and ability function.
To also respond to your remark about PLD and to give another example: I enjoy the fact of Confiteor being a seperate button because it feels more like a standalone and real (powerful) ability you get to tap every now and then, and feel good about it. While if it would just become a replacement for Requiescat when you're in that window, I'm sure it wouldn't feel as special just tapping that button again to get this Confiteor, while also considering that it's a different ability from Req in terms of function, so for that reason it'll also be illogical and thus perhaps less satisfying to me. Maybe it's silly and maybe it's nonsense since it's difficult to convey what I mean, but try to consider it.