Scarlett Jennings ultimately did not fight with the Big Ghost in front of the live broadcast.
Firstly, there was indeed no murderous intent on the other party.
Secondly, if they really started fighting, it would be quite a commotion.
Moreover, while the Big Ghost before her was full of resentment upon death, much of it had been worn away by her mother's final words and the passage of a hundred years.
As for why she still had so much uncontrolled Ghost Energy...
"You have absorbed the Resentful Energy of the eight previous generations of drowned baby girls. Though this Resentful Energy has greatly increased your strength, it has also affected your own Ghost Energy."
Her Thunder Talisman had only dispersed the portion of Ghost Energy formed by resentment, but as long as similar situations occurred, that resentment would continue to grow and influence the female ghost's actions.
Just like the commotion when the roof collapsed.