If Elayne did not go, the jailbreak would have happened cleanly, and everyone would have escaped, and it is possible they would not know about Master Lounalt being a Darkfriend, with access to Master Norry's intelligence-gathering apparatus. Every Black sister and Darkfriend who died in that incident, died because of Elayne's "impulsive" behavior! Also, who says it was only a jailbreak they were after? Every time Black sisters are involved in prisoner escapes in this series, they do lots of damage on the way out, like steal Horns of Valere, or put Dominion Bands on the Dragon Reborn, or sneak into Caemlyn and play 10 Little Indians with the Kinswomen. Elayne might have diffused a preliminary strike to soften Caemlyn up for the Trolloc invasion.

Your summation is wrong - she shows a great deal of heroism "when it comes to dealing with dangerous situations." What you call over confidence is actually calculated risk-taking (she is one of the most self-critical characters, with the least amount of confidence in herself) and her gambles almost always pay off. Furthermore, she sucks at "the art of governing," unless you consider that art to consist entirely of accumulation of personal power, regardless of the rights of the people you trample over.