Yes....I understand. But you may like to think that 'applying reason' is something people do uniformly and with uniform control over their biases and pet prejudices. That is not so.
Indeed, it is not something people do uniformly, which is why we need to encourage scepticism.
Everyone is not a sage with a perfect and dispassionate perception of the world, completely free of all emotional and cultural biases.
No, they are not.
Reason and logic are not super powers.
No, they are skills that (most) people can learn.
They are common abilities with severe limitations. Reason and logic can and do bend to serve our personal emotional requirements.
No, they don't. Reason and logic cannot bend. People can misapply them and can apply them inconsistently because of emotion or other bias. Another good reason to encourage scepticism.
They have a cultural element.... and what may appear perfectly logical and reasonable at one point of time can appear completely illogical and unreasonable at another point of time.
Again, that isn't reason and logic having a cultural element, it's people having a cultural element that can blind them to the logical and reasonable.
It is not skepticism that we should cultivate but.... Wisdom!
All the above suggest that we need to encourage people to detach themselves, as much as possible, from cultural and emotional connections when trying to apply reason and logic.
Reason and logic are not all of life, be when trying to assess claims of objective truth, matters of fact and logical arguments, they are the only show in town - which is, again, why we need to encourage scepticism.
I don't know what you mean by "wisdom" but it sounds suspiciously like an excuse to introduce emotion, culture and superstition into areas that should be dealt with by logic and reason...