I feel like she's been on that edge the whole way, seeing where she starts out makes us sympathetic to her though. I think some people saw in her what they wanted to see (a more pure of heart ambition) and for those people the ending is very bad. Yet because she was a flawed hero it's not nice and neat to deal with what Jon did.
The venn diagram of pure hearted, selfless and brave characters of this story has 2-4 people.
Another thing is the people she had been taking out throughout the series also made her a sympathetic hero, as Tyrion had outlined.
She took out Viserys (ok, it was Drogo that did that, but she could have intervened and Drogo would have listened to her. She had gained his respect by that point - which was the whole reason why Viserys got killed in the first place).
She took out at minimum Pyat Pree and Xaro Xhoan Daxos at Qarth
She took out the slavers of Astapor, Yunkai, and Meereen, in some cases with dragonfire, in other cases with crucifixion.
She took out the Khals alive at Vaes Dothrak
She took out the gold train funding Cersei and the Tarleys because they wouldn't bend the knee
She aided in taking out the wight army (although the final defeat wasn't due to her).
Up until she burned down King's Landing, she was sympathetic because she was taking out who the audience considered evil, or at least disloyal in the case of the Tarleys (even though Sam's dad was undoubtedly a ****). But what the show hid very well is Dany had ulterior motives for every single move, even if there was altruism in them:
In taking out Viserys, she removed her biggest potential rival (known at that time) and a person that abused her regularly.
In taking out Pyat Pree and Xaro Xhoan Daxos, she secured her, her dragons, and her party's escape from Qarth.
In taking out the Slavers, she secured for herself one of the world's elitist infantry untis as well as gained a loyal following in the people of Slavers' Bay
In taking out the Khals, she demonstrated she was the power of the land and secured for herself a cavalry (as unconventional as it was)
In taking out the gold train she weakened Cersei's financial position as well as her army
In taking out the wight army, she secured, if not loyalty, at least cooperation of the North and its armies.
In every single move that she made there was something in it for her - something that made her more powerful.