Ok so I just finished the college of winterhold story arc. When I first started I chose to go with illusion. In the storyline we found the eye of Magnus and and staff of Magnus. Is the storyline affected by your choice of school or does it not matter?
I have played that game over and over again and I have always gotten the same results as you, so I would say no. I believe the story is set on that particular part of the story line.
I've ran through these quest lines recently again.
From experience it appears that the quests are built how they wanted it from the start as when you go through specific dungeons you will find multiple scrolls needed to progress.
Example as you come through a dungeon there will be a frozen door that you cannot progress through without a fire spell, nearby is a fireball scroll. Later you would come across a door on fire that would then need a ice spell which again is a scroll located nearby.
I ran through on my most recent run with Illusion as a passive mage / berserking others to fight each other. Not once was Illusion actually needed.