While I don't agree with the idea that "he/she who wins in combat shall run the country", it fits Fereldens traditions. Their ancestors are the Alamarri tribes and this sounds like a very old tradition.

I don't like putting Alistair on the throne except for when he's engaged to Anora. I like him, he's my favourite character and has a good heart, he has his darker sides, he's emotional but I really don't see a good reason for putting him in charge of an almost destroyed country other than personal ambition. But that's just my thoughts about it.

However, Cauthrien being such a tough fight has nothing to do with her ablilities as a fighter. It is a game mechanic, they want you to go to Fort Drakon and while that part is fun, I always kill Cauthrien because my Wardens would not risk being imprisoned, so she bites the dust then and there.