I think that Daenerys is a character will the trappings of a character the overpowered fantasy character, but as the series progresses I think the narrative (in the books anyway) show that Dany’s dragons do not solve all of her problems. Her white savior complex is very frustrating to watch and at the same time I feel like by the time book five comes it shows that Dany’s intentions, as well meaning as they are, do not prepare her for ruling a group of people she has no cultural understanding of. A lot Dany’s doubt and internal criticism has been lost in making her one of the faces of the series and I think that is a mistake because she isn’t just Mother of Dragons. She’s a 14-15 year old who is trying to do the best she can, but has no experience in being a real ruler. I think I would hate Dany more if I hadn’t read the books because the show at times just gets her character wrong. Not to say she isn’t problematic in the books, she totally is, but the complexity of her age and her situation are sort of brushed over.
The Khal Drogo situation shouldn’t be blamed on Dany. I mean she was a kid, what was she supposed to do and HBO did decide to up the graphic nature of it for reasons that are confusing to this day.