There is no redemption for certain things. Doesn't mean that people who have done such things cannot be interesting and compelling characters, but they should not be presented as heroic. Using narrative conceits and the actor's charisma to represent a person who murders children as heroic is not something I care for. It is another thing to have antagonists who have complex personalities and believable motives, that is perfectly fine.It's not bullshit, it's (as eschaton wrote above) an example of a character being "a complicated person who is torn apart by a number of emotions, including duty, regret, anger, and determination." And love. And loyalty. He's done terrible things, yes, but also good ones. Jaime's redemption arc is one of the most interesting things about the show (and the books). And the same is true for the Hound (who started out terrible, but has changed). And Arya (who started out innocent, but has changed). And countless other characters. Really the only character in GOT who hasn't been transformed by his experiences is Jon Snow, but then he knows nothing.
And personally, the kind of complex character development GRRM writes is exactly the kind of thing I'd like to see in Star Trek. It's not incompatible with the utopian idealism of the Federation, or the pioneering spirit of Starfleet. On the contrary, I think it could be used to demonstrate those characteristics in greater relief with more convincing detail.
And in Star Trek in particular I want to see certain level of idealism in the main characters. Doesn't mean they have to be absolutely perfect, but yes I actually prefer my Starfleet captains to have pretty damn solid moral centre.