Due to the DRASTIC penalties that cut has vs armor, blunt/pierce does far more damage as armor scales up. Also, blunt and pierce weapons don't do much less damage than cut as it is. If you're only going to carry 1 weapon, you're better off with a blunt/pierce one.
I've been wanting a system for a long time where different damage types are better/worse vs different types of armor. Gives a reason to take different gear.