Then why have stats at all? Why don't you just say "we have thrown the rule book away and we are playing out a performance where it looks like we are playing D&D"? You can say "we are playing D&D RAW, but we focus on the role-play". But that is not D&D. It just isn't. If I was the DM, that char would be dead within a session. Of course, I would never be allowed to be near a group that tolerated such a char in the first place.
What is next, a 4 Con char? Would love, just love, to see a 4 Con Wizard actually played in a combat session. Or in your game, a 4 Con Fighter.