I like the general concept. My friends and I have discussed and done some things along those lines.

That is, the idea that what your character thinks they know about themselves, is what the player’s sheet shows. The GM then keeps the “real” character sheet.

Moreso, we also like not having players share character stats with each other, and try to speak about things in character and avoid using game stats when possible.

However we play TFT and GURPS, not D&D, and those games don’t have a Wisdom score. ;-) Those games are more logical and less fantastic, and more tactical – combat is played out in detail on a hex map, and your choices of what you do, and what the situation is, tend to be as much or more important that how strong your character is. No huge piles of hit points to know you’re necessarily safe from harm either.