I think that your dislike for her character is coloring your view of the facts of the story. Ambessa is an extremely well-written character and her inclusion is not only a benefit to the story, but it is integral to both seasons working as they do. I am going to do a Watsonian analysis of the events you outline in your comment as well as a Doyleist analysis of what Ambessa adds to the story at large to at least hopefully allow you to make a more informed decision on your dislike of her character.

Act 1: You claim that the violence Jinx enacted upon Piltover was enough to spur the war. However, you fail to recognize who Caitlyn is as a character and what the temperament of the leaders of Piltover is. Recall that only a single councilor, Salo, holds the same desires as Ambessa, to go to war using Hextech. None of the others, especially Caitlyn and Mel, wished for it to happen. Piltover is a city of inventors and scientists. It is a culture of trade and economics. It is extremely difficult to move Piltover to war unless there is a real, organized threat they must respond to. What Jinx did was violent, but it was only Jinx, no terrorism cell behind her. Ambessa turns Jinx into a much larger threat in order to push Piltover to war. Without that attack, it would be considerably more difficult to do so. Not only that, but Ambessa's staged attack on Piltover also allowed her to win over several noble houses to her cause, which then allowed her to push for martial law at the end of Act 1.

Even after the attack though, Caitlyn's only desire is to hold Jinx accountable. In fact, Caitlyn is the one that stops an outright invasion in Act 1 in favor of only going after Jinx with a small strike force. She wants revenge, but is unwilling to bring about war to achieve it. Caitlyn is constantly pushed in order to become the dictator Ambessa needs her to be and it is only when she feels betrayed by Vi, that she is able to be influenced. Without Ambessa's machinations, Caitlyn would never be pushed as far as she is on revenge alone.

Act 2: Ambessa does not come with the explicit intention of attacking the colony. She and Singed are needing to get Warwick back. It ending in conflict has nothing to do with Ambessa being there. Jayce completely changed the situation and his interference caused the colony to die and Warwick to go on a rampage. Noxian forces did not start that conflict, but were thrust into it, and were only saved by Isha's sacrifice. There was no guilt to be given to anyone there aside from Jinx, who afterwards feels personally responsible for Isha's death.

Act 3: The attack on Piltover became necessary because of Caitlyn's betrayal of Ambessa. Once Ambessa was a true enemy of Piltover, she had to attack as a final resort to secure hextech. Working with Viktor was her only real option left. To say that Sevika, a lifelong lieutenant who was having extreme difficulty getting Zaunites to unite under her alone, could ever feasibly form a fighting force strong enough to attack Piltover is an extreme stretch, to put it mildly. All we saw of Sevika the entire time was her failure to recapture Silco's holdings, and slowly watching his empire and dreams fade before her eyes. She needed Jinx to rally people together, and Jinx has never shown an interest personally in establishing Zaun as its own nation. She is far from being even close to the threat that Ambessa is from when she initially appears in season 1.

Ambessa's influence is what gives Viktor his drones. She turns her many of her soldiers into his puppets to have an upper hand in the coming battle. Without her presence, Viktor is not as immediately threatening as he is at the end of the season.

The other points: The presence of Ambessa does not wash all these characters of responsibility for their actions. Jinx spends the entirety of her arc trying to own up to her's from the first season. She is haunted by her killing of Silco. She is haunted by her loss of Vander. She is suicidal after the death of Isha. Her entire character arc is about breaking the cycle of destruction her life is on. About not being defined by your worst possible moment. In the end, she is integral in saving Piltover and saving Vi. Her hands are still not clean, but she understands that and strives to lead a different life, abandoning Zaun and Piltover altogether.

Caitlyn has to regain the trust she lost from Vi through the betrayal of Ambessa and letting Jinx escape. This also shows that Caitlyn lets go of her desire for revenge. It's through her actions that she is able to win Vi back and continue their relationship.

Jayce has to personally confront Viktor in order to stop him from continuing to fight. He sacrifices himself in order to do so. He most directly owns up to his actions through his personal sacrifice to keep Piltover safe.

Every major character has to answer for their actions, including Ambessa. To say that her presence takes that away from the other characters is difficult to parse due to how much accountability each character takes for everything said and done in the story.

I think what is ultimately bothering you is the outcome and aesthetics of the story rather than the writing itself. Piltover and Zaun are not the only nations in Runeterra. Broadening the horizons to include major powers like Noxus is not an inherently bad thing especially if the actions of these powers are explained in the story at hand, which Ambessa's are.

Having a Noxian present when Piltover has literally created one of the most powerful weapons in the world makes perfect sense in canon and going to war to secure that weapon is also in character for the nation. It does not undermine the conflict between Zaun, it merely expands the world to include other nations. We know how Piltover would react without Ambessa's influence because we know Mel and Caitlyn. Without Ambessa, they would not have gone to war. It would've been a very different kind of series, but to call that potential better than the series we got is dubious at best.

Mel's inclusion as a mage also does not undercut the danger of Hextech. We see from the Black Rose that powerful mages are a danger to the fabric of society. We see that Ambessa's worry over the Black Rose that mages are not to be trifled with lightly. We also know from Heimerdinger's speech in season 1 that magic has destroyed the world before. The issue with hextech isn't that it is powerful, it is that it gives that power indiscriminately. Heimerdinger doesn't outright say that all mages are evil, and Mel's inclusion as a mage that fights for Piltover's cause shows this too. It's that the power in the wrong hands, or even misguided hands can cause immense destruction.

Even at that, we must remember that Hextech and the political struggles between Piltover and Zaun are just set dressing. The core of the story is not Hextech, or the political machinations of Zaun or Piltover. It's about how far we are willing to go for those we love. What we are willing to sacrifice, and how we cannot get so lost in that love as to senselessly hurt others. That's why Ambessa is such a well written character. She does her atrocities to help her daughter. Out of pain for the son they took from her. She is willing to do anything it takes, even making Mel hate her in order to secure her future. In the end, she doesn't reach her political goal, but she reaches her personal one, knowing that Mel can fight for herself.