This really opens the rabbit hole up wide. Since you mentioned it, I'm going to throw out my stance on knives; they are completely different than guns.
I agree with you that training is not necessary, but a good idea, to use a gun in self-defense. A knife however, is completely different. In the case of a knife, I believe that training and continuous practice is essential to be able to defend yourself with it.
You see, a gun is a ranged tool. With it distance between the defender and the bad guy can be maintained. A knife is an up close and personal tool. Get in a knife fight and you will be cut. The only question is, how bad? Will it be a gash that can be sewn up by a doc or will it be a mortal wound? Ask any professional who teaches knife fighting and they will agree. If you find a knife fighting instructor who says different, run from them.
Oh yeah, it doesn't matter if you are the attacker or the defender, you're getting cut. I don't know the exact numbers, but they are high. Something like 98% of those who attack/defend with a knife cut themselves in the process and not just a nick.
A knife does have some intimidation value, but not nearly as much as a gun. Some will say that a knife can be used as a ranged tool as well. Yeah, I guess you could throw it, but the chances it will hit with the point are small and the chances it will stop the bad guy are even smaller. Then, once thrown, you have no knife.
I always carry a knife, but would not use it as a defensive tool. A stick that I sharpened with my knife would be better.