In short, because the game says so right now. Merging DWT and Bahamut is something I and a few other SMNs on this forum see as a necessary thing come 6.0 if SE wants to continue trimming buttons. Along that mould Deathflare and the Enkindles also are fitting targets for merging.

Brand of Purgatory is an AoE with a heavy hitting single target component while Fountain of Fire is purely single target. The numbers are tuned so that it’s always worth spamming both over Outburst or Ruin II irrespective of the number of targets. The intent is to simulate a short 1-2 Combo when you’re in Firebird Trance without cluttering your hotbars.