FrogReaver
The most respectful and polite poster ever
In a contest of wisdom, a Pc with a 19 only wins against a Pc with 14 about 40% of the time. Sure he may be a very wise individual, but the games math doesn't make him remarkably more incredible than someone who is only above average.
So the question becomes do you play to the reality of the games math or some
Made up fiction based on what you believe attributes to represent. Being that a 19 wisdom player may be very wise but still fails at rather mundane DC 10 tasks a full 25% of the time means that even one of the wisest beings on the planet in no way has otherworldly levels of insight and perception. Sure they are more aware than the average person, and by quite a bit, but they are no dhali lama. The games reality simply does not support such a claim.
Instead, in my mind, to represent the level of awareness of one like the dhali lama, you require more than just a high attribute. Such an intuitive character would be one who has trained their awareness so rigorously that they have taken the feats that grant expertise in the chosen skills.
I think you have that backwards. 19 wisdom should win more than 50% of the time on a contested check. Of course most NPC's won't have a wisdom stat to contest a check against and so the DM likely will set a DC.