It's more like denying Mario the Fire Flower.
Or denying Jackie Chan the use of his arms, legs, and whatever random objects he can find.
I also find it interesting that you're repeatedly insisting that Olórin's mortal shell being a big fish in LOTR doesn't equate to the same thing in HPverse, but haven't even considered the other way around. Not only is he powerful enough that he has to take on a weaker mortal form, but even in that form he is
still powerful enough to do things beyond the strength of even the strongest wizards. CJ brought up a good point earlier: Olórin,
in his mortal form, blew up a sizable portion of a mountain with lightning. He killed a Balrog in single combat while in the same mortal shell. There's nothing in HPverse that can compete with a Balrog as far as big, evil demons go.
Furthermore, you're relying far too much on disarming. Not only has it never been shown that
Gandalf needs his staff to cast, but the disarming spell works by forcing the target to involuntarily release their wand. In other words, it doesn't just accelerate the weapon, but also forces the target to open their hand; if it didn't, hands would be broken left and right, even in training. I think that a Maiar likely has sufficient force of will to resist a compulsion like that.
All that aside, Maiar are
also capable of disarming (or outright destroying) their opponent's weapon, and more importantly
they don't need to wave his staff or mutter fake Latin to do so. Reference the fight between Gandalf and Saruman. They knock each other across the room with little or no effort, and Saruman disarms Gandalf by holding out his hand. Sort of like how Gandalf later broke Saruman's staff by doing the same thing.
Also reference the fight with the
Balrog. After Gandalf falls, he retakes Glamdring, we never see that staff again after he drops it, and he later turns out to have killed the Balrog. Without. His. Staff. Incidentally, we also see him call down a bolt of lightning and charge Glamdring with it without so much as a glance.
So let's recount:
Powerful force pushes, calling down lightning, smashing a mountain open, killing a demon, firing a blast of
something to drive off the Nazgul, and let's not forget the magic sword and fireworks. All that without incantations, often without a staff or any significant ritual, and that's just the skimmed bits off the top of my head.
Even for a mortal magic-user Gandalf is extraordinarily powerful. Mind you, Dumbledore isn't a pushover, but Gandalf is much closer to a high-level, efficiently min/maxed character (or, alternatively, Nanoha-tier) than Dumbledore is. Everything cited as a strength for Dumbledore (experience, casting without a focus, danger in the short-term) is also a strength for Gandalf but more so, and the latter also doesn't need any vocal incantations. And he has a magic sword that he can use to do Highlander impressions.
That said, they'd never fight, because either they're timeclones or Dumbledore is a fragment of Gandalf's soul that was lost when he died fighting the Balrog.