I disagree. I don't think Two-Face's actions in TLH/DV were motivated by a desire to save the city. When Dent was scarred, it revealed to him an utter failing in the system he upheld. Unable to believe in justice any longer, but also unable to turn his back on everything he believed in, he broke in two. With two equal voices, he was unable to make judgments, hence the coin. Harvey may have still wanted to save the city, but not Two-Face.
Sometimes I wonder if the Two-Face persona even has motivations. I wonder if it's not just pure resentment, a juvenile sort of lashing out. It does whatever it can to create chaos, because it's an entity made entirely out of the anger and misery of Harvey. It's not about revenge, it's not about anything--it's just a persistent condition of hate that has a voice. Two-Face exists because Harvey could not conceive of venting what he was feeling, and so he created another persona to do it for him.
It took me a while to figure that out. I was always thinking "Why does Two-Face commit crimes? Why does he do anything he does?" The problem was that I was thinking of the Two-Face persona as a part of Harvey Dent--something that, in some way, is influenced by who he was. A sort of darker Harvey. But that doesn't follow. A darker Harvey wouldn't rob banks or kidnap twins or any of that. Accordingly, Two-Face must not be at all like Harvey Dent. He is a different personality entirely, not motivated by anything in Harvey's life, or any darker versions of Harvey's feelings.
One issue I have is that most writers ignore Dent entirely. Sure, he flips the coin to decide whether or not to off Batman, but what about before that? Why don't we see Dent sitting in a basement somewhere arguing about whether they should A) turn themselves in, or B) execute some crazy scheme? Two-Face is always depicted as being in the driver's seat. You never hear Harvey say "Screw this, I don't want to run this gang. Nuts to bank robberies. I don't want to steal that shipment of Doublemint Gum."
Two-Face is often written as one mind that simply can't decide whether or not to use lethal force. This shouldn't be the case. When Two-Face says "Let's put Gordon on trial!" Harvey should say "Nuts to you." I would like to see some coin tosses land in Harvey's favour, I'd like to see Harvey drive for while, only to have his plans twisted by Two-Face when the coin lands scarred side up. What is Harvey Dent thinking when Two-Face is running amok? What would Harvey do instead, if the coin favoured him? How would Two-Face twist that into something terrible?