I think we can all agree that at times the training is a bit too...abstract at times. Personally, I view the training system as a bit of a hack since the skill leveling system has always had some significant problems with it. Armor levels up poorly, some schools of magic do a bit too. And frankly, is it really more realistic to sit in town and cast "Detect Life" or levitate objects for a couple days or more to become a master of alteration? A lot of the skill leveling stuff is wonky in general, and training just provides a way to avoid that wonkiness and help alleviate problems of leveling up non-combat skills and then being too weak to deal with bad guys properly (you can then train combat skills to lessen the problem more quickly).
Similarly, becoming the archmage and being the archmage also has a host of problems. I'd hope at some point they realize that this process should make a bit more sense. There's nothing wrong with being a respected member of a society like All-Father8420 said. If you don't get to make any decisions as a leader or do anything as a leader, then there's no point to letting you become a leader.
Funny that you commented that the journey is what is important. Then when I comment that becoming leader by some mysterious guy going "you should be leader" and another person then going "yeah, you're leader now" you seem to think I shouldn't have a problem. There's a distinct lack of journey right THERE. Note, I don't have a problem with that guy's comment, or Tolfdir agreeing...it's the extremely casual and off-handed hand-off that concludes with that's bad. Frankly, there should be more involved in it at the end. I would note that I do enjoy the rest of the quest-line and I think overall it is good...just the archmage part at the end is poorly done. This seems to be a problem in many, but not all games. As if upon becoming leader, starting a relationship, or whatever, no problems or new conversations should happen. (Yeah, Bioware sometimes has the same problem). There needs to be at least a bit of action once you've reached a goal that properly demonstrates you've reached it, especially if that goal involves more responsibilities. That or the game should end and you get an epilogue or whatever.
Edit: I don't mean to say I don't think there should have been more breadth to becoming archmage either. Clearly a few more quests for the various school heads and such would make sense. I like the main questline, but it doesn't feel natural becoming an archmage at the end of it since it requires almost no magic.