While you're partly right, Diana said the entire time that she needed to kill Ares to stop the war, she just didn't know who Ares was. Of course the evil looking guy inhaling some weird mist and getting super strength is the one she should be going after, right? While he was in charge, he wasn't the person she was looking for and when he died it didn't influence anything.
While Ares did just give people whispers and ideas to start the fighting, he also had a power over them. At the end of the movie, after he was taken down, the German soldiers were celebrating with Diana's crew. They didn't just shake off a fog, they were actually friendly to each other.
Yes, we know that humans are pricks, but in this case Ares seemingly had more influence over them than just the whispers he spoke of. It's not normal for a plane to explode and then the soldiers just shrug it off as if everything's gravy and they are suddenly cordial. Of course we as watchers know that WW2 happened, but the impression given at the end of the movie was that WW1 was over now as they were in talks for peace before.