Where did these so called BNF's get the idea that Hound would be sworn shield of Sansa in WF? That he would be true knight by serving he and gonna redeemed by Sansa's soft power. Imagine Sansa's inner thouhts: 'He almost raped me, harassed my sister and Jeyne and brutally killed Mycah. But he is sorry so all this is forgiven. Let me make him my personal bodyguard and I have to forget my trauma given by him. Oh Brienne, you are not my true knight now even though you are better than him."
Sansa has trauma? The Hound needs redemption? Pah. You classist dummy.
If you do a little brain-stretching exercise called "Sansa is always wrong", you will be able to ease into the mindset that makes the ideas you mention in your ask possible.
It doesn't matter what someone else does to Sansa, because she is always wrong, which means they are automatically right. Or at least, it makes her responsible for their actions.
Arya, Ned, Joffrey, Robb, the Hound, Cersei, Tyrion, Littlefinger... It doesn't matter who. They are right. Because Sansa is always wrong. Internalize it.
Sansa rewarding the Hound's valiant attepts to "open her eyes to the reality of the world" by making him her sworn shield (you know, like he was for Joffrey!) is really the least she can do to repay him.