How does one “earn” self-righteousness?
Yes, this is exactly the point of his character. In a generic extruded fantasy product he would be the heroic paragon with his own code who always makes the noble decision no matter what the lily-livered lickspittles say and always wins against the odds. But George Martin wanted to have a little fun with this particular idea, and so in GoT he ends up with his head on a spike. To be fair, back in 1996 the fact that Ned gets himself killed was a shocking twist, rather than “Of course he got killed because this is how things work in GoT”, because GoT didn’t exist yet.
Inasmuch as professional wrestlers count as “TV characters”, I submit for your consideration John Cena.
He has, on at least one occasion, threatened to do a terrible thing to someone in an I-Quit match (like an Attitude Adjustment finisher off the top of a car), only for his opponent to say “I quit” to end the match, only to do it anyway. (Batista.)
He also apparently demanded a match with good guy Rey Mysterio for the WWE Title only two hours after Mysterio had won it from The Miz back in 2011, forcing Mysterio-- who’d fought a grueling contest to win the belt for the first time-- to have to face a fresh Cena for the title.
Neither of those actions make Cena look like a nice guy.