What you need to understand is that, in real life, you can do the right thing and still have consequences. That's a lesson that GoT is big on conveying to the audience. I have two similar examples for you:

1) Have you seen the Martian? They show this really well. Going back for Mark Watney was arguably the correct decision. It worked and everyone survived. But if I was the Director of NASA, I would never trust any of them to obey my orders again. They've demonstrated a willingness to defy me. How can I put them in a position of trust again? It's worse BECAUSE they succeeded. It will embolden them to commit future acts of insubordination.

What they did was good, and they should be rewarded, but they can't can't be trusted again in the position that they are in.

2) Another good example in a book I just finished reading called Theft of Swords ... the main character is an epically good swordsmen who works as a thief. He is hired by the rightful king to help stop a coup and gets into a sword fight with the second-best known swordsman in the kingdom. He is fighting the guy, apparently just barely holding him off, and then the first-best known swordsman comes in and finishes the job. Later, #1 says "I saw you fighting ... you were toying with him. Why didn't you end it?" Later he explains that "there was no way I was going to strike down a nobleman. Everyone would have cheered because it was the right thing to do, but later, they'd have realized that a commoner spilled noble blood. They'd have had to come up with an excuse to execute me. Killing nobleman is bad business!"

So, again, the right thing was to kill the traitor. That doesn't mean that everyone is going to be ok with exactly how it happened. Commoners don't touch nobleman, no matter the reason.