I cant see that sytem working with the College quest line.
That's true. Beth would have to go back to guilds that are actually interesting and involved where you have to work and advance up the ranks; instead, of the current join guild, do a quest, do a quest, you're the leader now crap that they have.
Player shows up to save the day but is stopped because his healing spells takes one second to long or his enchants are three charges short of necesary according to spellcasters local 402.
it's not perfect, but it's infinitely better than a system where a mentally challenged Orc that can barely cast any magic becomes an arch-frelling-mage.
To me its garbage in garbage out.If you put in minimal effort and blow through the questline thats on you.If it works for you it's your game enjoy it any way you want.
It's hard to not "blow through" a quest line that has a pathetic number of quests and is constantly telling you "DO THIS OR UBER BAD THINGS WILL HAPPEN!!!!"
You would tutor a student in whichever school(s) you want and your skill would determine how much that student learns.Say you need to teach a total of 100 points of learning to advance if you are proficient it wont take long if not you can teach 100 students 1 point.
Those that focus on magic will have an easier time those not so much will have to grind if they wish to progress.
That sounds like an awesome idea. You being the trainer for a change.

I had a Fighter in Morrowind who was Arch Mage of the mages guild. I think she knew enough spells to do whatever enchanting she needed.
Regardless, she had the knowledge since there were skill requirements. Whether you put that to use or not doesn't change the fact that you knew how and were a master in at least one of the schools of magic they taught. Again, it's not perfect but it's better than what they have now.
Thief-assassin build in Oblivion Arch Mage who knew very little magic.
Yes Oblivion has this same flaw.
Basically you're an administrator. Look at it that way.
If you were an administrator they'd call you an administrator. Since when do paper pushers have to practically save the world to get a job? If all the quests had you filling out paperwork and other bull like that then maybe I'd buy this administrator crap.
It seems that every criticism of Skyrim on these forums ends up breaking down to people saying "MERRERWIND WUZ BETTER!!1"
A simple reason for that would be that Morrowind did some things better; like it's guilds.
Not to mention making the dragon-born archmage isn't really that bad an idea, The dragon born is the single most powerful user of the voice in the entireity of skyrim, So not only is the dragonborn a master of a school of magic, He's the master of a long-dead school of magic.
It's not a long-dead school of magic. Plenty of others use it just fine. It is also not an area of magic that the College of Winterhold studies, teaches, or practices. There are already two other places in Skyrim that teach and practice the voice. Again, if you were putting together a baseball team would you pick players based solely on how good they are at playing basketball? They're both sports right? That one guy is an insanely good basketball player so obviously he should be made MVP of a baseball team right? Eventhough he's never played baseball before?