Wisdom reaction question

After taking a careful look at the core book, something struck me as awkward about the way the Wisdom reaction is determined. It is based on Bearing or Wits, but the description of Bearing does not seem to indicate anything like "common sense and . . . insight" (core book p. 49). However, Perception does cover "your awareness of your surroundings, including your ability to spot what's hidden" (core book p. 47). "What's hidden" could be said to include things that cannot be seen so much as sensed. Hence, why the Sense Power spell is based off Observe, which is modified by Perception.

Would a reasonable change to the Wisdom reaction, then, be the better of Perception or Wits? Why or why not?

PS. My ideas for revising CODA's magic system have been edited and put together in a clearer, more cohesive form. I've also included and expanded some ideas I got from the responses I received. Let me know if there are some glaring oversights I need to tend to or if you have questions about how it works.

Fine, but Wisdom is based off Brg or Perc, not Wits :)

I can see your point on Bearing, though.

Saruman was intelligent and cunning, but was he wise? Denethor was intelligent and cunning, but was he wise? The Witch-king had to have been intelligent and cunning as a mortal man in order to master dark sorcery, but was he wise to do so? Aragorn was no cunning magician, but he was wise. Sam was certainly not especially intelligence, but he was wise.

I think one of Tolkien's themes is to distinguish between overt marks of intelligence, shrewdness, cleverness (all things we like to congratulate ourselves for being) and the internal force of wisdom (that inner voice guiding us to what is right and true). In that sense, a person's nobility of presence (his "bearing") helps him resist the flattering lure of cunning power--so in that sense it is akin to wisdom. This is why I use Wisdom tests whenever characters may reflexively perceive that something is wrong: it is like those "my heart tells me..." moments in the books.