But then i realized that i am a master of the Thu'um, that is pretty fancy and skilled magic.

All my toons are "multi-taskers". They all do some of everything, it's just more fun that way....

I'm a fan of roleplaying. But it annoyed me to see that ''visit the college of winterhold'' quest.
So i came up with a reason to join, and that is to understand more about magic. And to study the Thu'um.
And since shouts are magic, then i am very skilled in some sort of magic. And it looks like i am skilled enough in that sort of magic to be Arch-Mage.

And I roleplay my girls as having been on their own in a hard world from a very young age, which means they will do what they have to do to get ahead not to mention stay alive....

My current toon is the warrior type. He is currently wearing dragonbone armor with magic enhancements. He recently became the Archmage, although he love the feeling to wear the archmage robes, he decided to stash it away in his inventory until after he defeats Alduin. He will then dedicate his life to study and to help people to learn and to master the art of magic.

Same here. Hybrid builds are just more fun to me, and this is usually how I justify them dabbling in everything and figuring out what works and what doesn't.

I have never made a dedicated magi character in this game. They just seem so weak. Having to go to the college just to finish the main quest is silly.

When I play, I don't limit myself to any content, no matter the character. Meaning litterally any of my characters can join the college of winterhold

The only problem is that you become the Arch-Mage to fast.

But like you said, the Dragonborn is the Master of Voice, and it's considered as a type of magic.

Personally I made my warrior toon also a master Enchanter.

I cannot NOT be the Arch-Mage with any character that gets wheeled into Helgen for execution.... It's my favorite setup with all the storage, vendors, and crafting ingredients and tables available. I just like it there.
My experience is that I became Arch-Mage for pragmatic reasons, after a series of unfortunate events; and Tolfdir's personality is much better suited to being Master Wizard and mentor to the newbies like an RA. I have dinner with Tolfdir now and then and he advises me to rise above some of the pettiness at the College.

Plus, early on and for quite a while afterward, in that courtyard you cannot swing a dead cat without hitting a dragon.
If you've advanced the MQ just enough to trigger the dragons, that's where you want to be.