As anyone would pobably agree the mages quest line is a mess. You go around not really learning anything about magic, acting as the delivery boy for the other NPC's as they do the important research and it all ends with you becoming archmage despite never working for the position and having no qualifications besides being the player. But I guess that's what mods are for, so if someone, anyone, would be willing to fix it I'm very sure thousands of modders out there would download it in a heartbeat.
The best way I could see this working is if the "First Lessons" quest was split into two parts, after learning wards in class tolfdir(instead of taking a group of unprepared students into a dungeon they know nothing about) simply dismisses class and the quest objective becomes Learn the basics of magic.
From then on you can visit the arcanaeum and find or buy research notes of different teachers that start small quests like "test the effects of fire magic on 3 draugr" and at the end you get a small permanent perk like "fire and turn spells are 10% more effective on undead". After completing a set number of those quests and gaining at least a 40 in three schools of magic, oyu complete "First Lessons" and "immediately start "Advanced Lessons" where the quest objective is speak to tolfdir. He starts the "Sarthaal" quest, then after getting to the point where you inform him about "Night of Tears" he dismisses you with a reward so he can continue researching the Orb.
You the go back to the arcanaeum where Urag, having a better opinion of you after helping him recover the stolen books, tells you about the hidden writings of shalidor and the lost books quests, but instead of paying you a random some of gold he trades you research notes from retired mages and archmages. These notes start small quests like "find quest incredient X, Y, and Z and combine them in a cooking pot after using one of shalidors scrolls to make a potion that gives you a permanent 15% damage increase to destrustion spells"(said potion can only be made once and while you have the quest), and like before after achieving a set amount of these quests and having at least a 60 in three schools the "Advanced Lessons quest is completed.
"Hard Lessons" starts up and you talk to tofldir again, and he discusses with you about the Eye of Magnus before the series of quests that lead you to learning the staff of magnus's location. After coming back with everything normal, you give this information to the archmage only for him to tell you that laberynthian is a place where he'd be reluctant to send a master let alone an adept like your character, but he does reward you for your work by naming you as a professor and giving you a room in the hall of countenance. You are now able to trade the research notes you've obtained from Urag with other teachers for knew quest such as "Find a way to harness power from the Eye" where after drinking a potion of amplify destruction and using a duel cast electrical spell on it you gain a permanent 50 extra Magicka.
After completing a set number of these quests and getting 80 in ALL the schools of magic "Hard Lessons" completes and "Final Lessons" begins telling you to speak to the archmage, only to find ancarno messing with the Eye and the normal mages quests proceed to the end with you becoming archmage. Then after gaining 100 skill in all schools and completing all the master ritual quests "Final Lessons" completes, with you coming into your title as the legendary Archmage of winterhold.