Give me some hard mechanics here. I am not arguing that wisdom should not exist. Common sense and intuition is a skill called sense motive/insight. Sense motive is a saving throw against lies, it can give you a hunch, it can detect enchantments, it can figure out secret messages.
Wisdom is too broad in its application. It sort of grabs random knowledges and puts them there (Heal, survival, dungeoneering, and profession). About the only skill I think could be argued to be there is sense motive/insight.
3.5 WIS skills
Spot
Listen
Survival
Profession
Heal
Sense Motive
4e adds:
Dungeoneering
So perception, will save, divine magic, knowledge, hunches, lie detection, sensing enchantments, discern secret messages, and psionics (in some editions). To me that seems like a hodgepodge of stuff. It is not like STR, DEX, CON, INT which are all easy to understand and you know what they will mean mechanically. WIS and to a lesser degree CHA you have no idea and it varies based on edition.
Other similar stated games chose to go in a more definitive route. Physical stats in these games are the same but mental stats differ:
Call of Cthulu (intelligence, education, power, appearance)
Traveler (intelligence, education, social standing)
Alternity (intelligence, will, personality)
I think 6 scores is enough to model the game well, I don't think you need anymore than that.