"Traditional" roles do NOT restrict mages to a single school. My mage hasn't touched a weapon other than bound weapons.
Gandalf's role is arguable. He WAS a wizard, thus a spell-caster, though Tolkien did cast the Istari in a more mystical role, their "earth forms" were of wizards (probably going back to the druidic kind of demi-god status of Merlin). In his form in middle-earth, Gandalf was, inarguably, mortal (killed by the Balrog, brought back by Galadriel) and wileded magic. YOU might not think of Gandalf as a traditional mage, but DnD as developed by Gygax and Arneson CLEARLY used Gandalf/Merlin characters as archetypes. Even Tolkien ascribes "wizard" to Gandalf. Although, originally, Gandalf was quite a different character (more like a dwarf, but still a wizard).
Clearly, you have not played 1st ed. DnD or AD&D, talking pre-Unearthed Arcana even. Pit an equal level mage against an equal level fighter and the end result is nowhere near a foregone conclusion. BTDT. I haven't PnPed in many years, but more than a decade of PnP experience, probably 2 decades, tells me you haven't PnPed much if you think a mage is any more god than the fighter of equal level.
/Offtopic
Of course, It must be pointed out that Gandalf never used Glamdring in his spellcasting and, as the Grey, was doing things like fending off the Nazgul and creating firestorms; plus he feared using his innate power openly since Sauron would notice. And no, Galadriel did not bring him back; by all accounts he was alive when Gwahir sent him to Lothlorien. Eru Iluvatar sent him back. As for Gary Gygax, he's famous for his "The One Ring is just a Ring of invisibility" comment, so his understanding of the metaphysics of Tolkien's world is under question. Also, fun fact: sorcery in Middle-Earth is the manipulation of the corruption inflicted on Arda by Morgoth.
As for Pnp wizards...
AHAHAHAHAAAAAAA!
Oh...wait...you're not joking.
Wizards turn fighters into bloody smears on the ground. Level 20 wizard>Level 20 fighter.
Or Level 20 wizard = Level 20 cleric = Level 20 Druid>Level 20 anything else>Level 20 monk. There's a reason D&D's well knwon for Linear Warrior Quadratic Wizard, even in 2e. Not touching 1e, as it had all sorts of issues with it.