Lars said:
Why do you say that? Bara doesn't really have all that many "after you win a power challenge" effects. And most of the ones they do have are "win by 4" effects, which a power challenge version of Feigned Retreat or Misinformation would not help with. Short of the plot, automatically winning a power challenge with the event wouldn't help Baratheon capitalize on the power challenge all that much. Certainly not as much as Stark on MIL or Lanni on INT.
If anything was deemed "too strong" with these events for Bara, I doubt it was their ability to capitalize on winning the power challenge. If anything, I'd think it would be Vigilance that was deemed too strong, which means the cycle would be more balanced if Bara didn't win any challenge type automatically. Oh, wait.... 
Plus, look at the Dominance direction they seem to want to take Bara in with this cycle: The Iron Throne, Zealot of the Light, Acolyte of the Flame (think about it...).