LotR -- Book 2 - Chapter 07 - The Mirror of Galadriel

[Imladris]

But Galadriel was able to keep her emotions under control sufficently to perceive the folly in his words.

Control of emotions does not equal wisdom.

Maybe there are different kinds of wisdom? Sort of like the brainy professor who has no sense and the student who has sense but isn't the brightest bulb...Sense and brains are both "smart" -- just different kinds of smart.

Thus maybe your definition of "wise" is not the definition Tolkien had in mind.