Hand holding? Limitation? Having a guy say "no, if you haven't enough skill in at least one school of magic you can't get a higher rank in this magic studying institution" or "you only know bam bam smack slash, you not great guy here because you not mage" isn't hand holding nor limitation.
If I'm a poor and homeless adventurer and I am in Winterhold, why wouldn't I ask for work there? They teach me a basic spell for free, and then send me to a place where I can find great rewards and I can just slash my way to get them. Why a poor, homeless axe-wielder has to run away from a basic quest where he can get money and where he can use his preferred means to do it? Then this guy is forced to save them and become arch mage, because who wants to let the world explode or those mage guys die, if it's a kind and good-hearted person?
Speeking with the archmagister at the begining of the quest line, he tells you he only desires that the college stays focused on the study of magic. not that everyone that goes there is turned into a mage of such repute they could be the emporers new court wizard, or lead a battalion of battlemages or become a professor. Just that the college remains a place for study, and that the students follow the rules in place to keep the place safe for such study. thats it.
If I don't WANT to lead the college, but I have to do it anyway. And of course not everyone is turned in the mightiest mage ever. But that doesn't mean that the no-brain guy is the best leader they can have. If you know nothing about magic, you're going to be easily decieved by those who do know how to use a spell. And if you doesn't know anything about magic, you won't be able to administrate the school as well as a guy who knows what the students need to study.
And they had known me for a week. How do they know that I am a good guy? I might have saved them simply because I thought that then I could influence them to do my will. And how do they know that I know how to manage and lead anything? I might be the dragonborn, but I might as well went to Winterhold just after I scaped from Helgen. Nobody knows I'm Dragonborn.
