Ok, so the base question seems to be "What is the Mage's Guild?"
So, if I may be excused a grammar digression, "Mage" is the root word of "Mage's" and "Mage" is the root word of "Magic". Well, by transitive property of Old French, Greek, and Ancient Persian. Anyway. Mages are people who are all about magic. Learning, using, studying, disseminating, controlling, etc and so on.
So I'm thinking something closer to TESII, where there were (poorly-implemented) factions within the Mage's Guild. Let me use quests as anology. So let's say you've got Orcy McOrcFace. He's an Orc. He likes heavy armour, and heavy weapons. What's he got to do with the Mage's Guild? Lots.
So some mage found out some fancy gizmo they want is being held by a bandit chief. The gizmo is, say, a magical claymore. Now, the mage wants it to study it, because it's a good example of its kind. So he hires Orcy McOrcFace to "Kindly retrieve the item. I'll give you Xk gp." Now, at this point, Orcy McOrcFace goes out and murders the bandits, grabs the gizmo, and at this point, has a choice: Keep the claymore (gizmo), and take a reputation hit, or return it, and lose the neat weapon, but gain a bunch of gold.
This is the sort of quest a pure fighter-type could get from the Mage's Guild; and, in fact, might be a high-ranking member of the Retrievers (or whatever). Very well-paid, but they have pretty much nothing to do with directing the day-to-day activities of the guild.
OTOH, a there might also be Field Archaeologists who delve ancient ruins to find lost knowledge. All stuff the PC could do, and NPCs could have as a profession/faction. All pretty pie-in-the-sky, but if TESII-style quests make a good, and improved, comeback, it could be done. So, in short, the Mage's Guild might be a loose association of people whose primary interest lies in magic stuff, whether that stuff is finding/buying/selling magic items, making magic items, doing research, whatever.
...Does that make sense, or do I need more sleep?