the expert with a knife will beat an unarmed guy every time. Unarmed knife defense is for use against people who aren't trained. Against any other level of skill, well it's pure darn luck if you survive that.
I agree on a functional level - waza, technique, capabilities of harm of the weapon vs. unarmed.
BUT - there is a certain attitude - kiai - which is specifically trained for in martial arts - and I think particularly within Japanese martial arts - which is exemplified by the expression, "Whatever happens, I'm going home tonight."
There are, I think, three wings of esoteric training in Japanese martial arts:
1. internal training (a lot said about that these days, and even practiced as well).
2. "Spiritual" - including mikkyo, Taoism, neo-Confucianism - the transformation of the human being who is practicing, for tactical, moral and religious/spiritual purposes
3. Kiai - the development of will and the ability to focus one's being to achieve a goal - in this case, the bending, the manipulation or the shattering of the other person's composure or combative ability.
I mention this because it has, on a personal level, saved my life, and also because this is one of the neglected areas of study, even in modern-day koryu. Without kiai, the best waza in the world will not take you very far. With it, you can sometimes overcome the "superior" fighter. This last statement is factual. Your attitude in such circumstances, does not include the word "sometimes."