In the knife world, and perhaps kitchen knives in particular, you'd get steering if you didn't make sure the edge met what was to be cut with a symmetrical cutting edge.
Now, the Japanese cutlery (I'm talking double bevelled knives here) in particular is designed to be e.g. 80/20.
They do have minute differences in their whole grind on each side though, to make up for that.
That is by design, it helps in food release amongst other things.
So a knife like that is made for left hand or right hand use only.
Well, often anyway.
So no, symmetrical isn't always desired in a cutting tool.
Kamisori's and single bevel knives is a whole other thing as well
