Alright, I like a good debate so why not...
Leadership is NOT a trained ability? Knowing how to run a nation isn't something you learn? Are you serious? While some people have a natural talent for it, they still need to learn HOW. It's not something that is easy, nor is it something that we're born knowing.
No, what I said was that training isn't as important as experience. People straight out of theoretical training are generally not thrust into leadership roles but work their way up a ladder. This training that a HN or DN warden would have is largely meaningless in the face of a lack of a lack of actual on the ground experience of leadership. Not to mention we're ignoring all the other origins in the game of course
And I would just assume that the child of the second most powerful man in the nation would be raised in such a way that they know how to run things as well. After all, when your father and older brother leave, you're left to, ummm, run the teyrnir. It's not quite the same as, say, your parents leaving their kid alone for the weekend. You are left to run a major territory with a skeletal army. I cannot imagine you HAVEN'T been trained.
You're being left at home to run a basically empty castle. My impression from the HN origin (its been a while since I played it) was this was your first time in a leadership position and you were sort of being eased into it. In fact one of the dialogue options with Mama Cousland was asking her to stay and help you run things as you weren't sure you could. But all that is besides the point- in my opinion the training is nowhere near as useful as you're making it out to be, frankly. This is as someone who has been thoroughly educated in leadership and organizational management.
Edit: Since you didn't like the medical training, how about telling a new lawyer how to practice law? That may be more apt anyway, though I would think that governance is a bit more complicated.
I think we're approaching the concept of leadership and politics in different ways. I think leadership and political skills are required in any senior position in any field whereas you seem to be arguing they are similar to a profession. I would not take professional advice from someone senior in another field, but I would definitely be open to leadership/politicking/management advice.
Edit: And age does not equal education nor wisdom. It means life experience, but when the majority of that life has been spent in a sheltered circle, you're not even going to have much of that.
Sheltered Circle? Hmm I guess again that depends how you saw things. I saw the Circle as a combination of university, research centre, military academy and monastery (of sorts), with quite sharp, cut-and-thrust political maneouvering required at the top end. At the First Enchanter/Senior Enchanter level, from all the clues in the codex entries, I thought that implied plenty of political and leadership skills would be required.
Yet another edit: Can't you like Wynne but acknowledge her flaws? Wynne talks to hear her own voice, even when she has nothing to say 
Yes she has her flaws of course, but the argument was started when it was said that it was stupid of Wynne to give the Warden advice.