I was commenting about the fact the trial of combat thing even exists in the story world at all. It's such a convenient thing that as you said it, we should have seen it coming a mile away. Pretty much every single accused in the story world that is losing their trial would be dumb if they don't invoke it. I mean, what do they have to lose?
a trial by combat request can be denied, though it happens rarely... you'd also run the risk of two people dying instead of one (you and your champion, rather than just you), assuming you can find a champion at all.
and sometimes, you can just get screwed over.
funny non-spoilery backstory:
Prior to the start of Robert's Rebellion, Lord Rickard Stark, demanded a trial by combat when called to answer for his son Brandon Stark's alleged crimes. King Aerys II Targaryen declared that the Targaryen champion was fire and to prove his innocence, all Rickard had to do was not burn.