The broader point that I would like to make about this is that simply adding Bahamut to DWT isn't doing enough. No matter which of the two scenarios is chosen, there are many, many other things that would have to be adjusted to make things work; I simply believe that separating Phoenix allows for more freedom in design.
Summoner needs a phase like DWT to weave everything that it has and give the player some relief when it comes to unpunished movement and that phase needs to be able to be used freely. You say that FBT provides you with 20s of mobility, which it does, but that mobility still comes attached to your biggest damage output (thus can't be delayed) and is still punished because of the Demi-summons and their problematic movement that can cause the loss of their auto-abilities. Add Bahamut to DWT and now you have the same problem on both ends of the rotation and no simple instant-cast phase to give you any relief. If Demi-summons could ever be fixed to not drop their abilities when you move or have an arbitrary delay upon their summoning where they won't respond to your action, then these phases would be free of any movement punishment, but that still leaves us with a very problematic 40s of downtime between them (to say nothing of those damage phases being tied to the strict 60s cycle still). With only being able to weave Energy Drain and Fester/Painflare during a Demi phase, this means that all four Egi-Assaults must be used in the 40s between trances, along with Enkindle, Devotion, Tri-disaster, and the other ED and its two actions, with only the four Ruin IV procs, swiftcast, and a hard-casted Bio III to use as means to not lose damage while weaving. Even if you try to mitigate this by removing Egi-Assaults, what does the rotation become at that point? Even more of a Ruin III spamfest with even less interactive pets?
Removing Phoenix from its trance breaks the cycle into more manageable parts and that is the point I'm trying to make. Imagine the rotation at that point in its simplest terms: Trance -> Demi -> Filler -> Repeat. You begin with a trance to weave in all of your Egi-related abilities, you move into a heavy-hitting Demi-summon, then you fill the gap before your next trance with whatever needs to be done. Except that's being rather restrictive, as the only thing that can't be changed (If trances are still tied to a 60s CD) are the trances themselves. Those Demi-summons could be used at any point in the 60s cycle, as long as you're not delaying the use of your next trance. It's my belief that turning the rotation back into something like this allows for much better design going forward, as each phase in this case can be adjusted more freely to feel better to use while trying to come up with new mechanics to ease the 40s downtime phase in the other scenario could create even more problems.