Kiai refers more to our "spirit" where as kakegoe is actually the yell.
I'm not sure why sensei scream "KIAI!" to tell students to yell louder. But actually, kakegoe is the expression of kiai.
Kakegoe is like what a basketball player does after he 360 degree, behind the back, under the leg, slam dunk over Lebron James at the buzzer to win the NBA Championships. He's yelling and pounding his chest like the alpha gorilla on the court because internally he feels like he single handedly cured cancer, ended world hunger and rescued a kitten from a burning building all at the same time. If we can build up and take that kind of energy and use it to actually do something good as a dojo that would be __(fill in the blank)__!
Why is kakegoe important?
Kakegoe can help one to:
Concentrate power toward one point and generate more power than usual like a laser
Overwhelm the opponent
Crush the opponent's spirit
Puzzle the opponent
Lure the opponent out
Irritate the opponent
Surprise the oppenent
Let the opponent realize your victory
The above (except the basketball analogy) was shared by Hasanuma-sensei, a CKK sensei in the 90's who has since moved back to Japan. He is still very active in kendo, often seen time-keeping at the All Japan Kendo Championships and participating in other events.
After reading this, in my own reflection as a leader, I recognize that a soft kiai could be a reflection of a soft spirit or internal, emotional, psychological and/or spiritual state of being. So, when a person's kakegoe is soft, I ought to wonder what might be causing them to feel that way on the inside. I ought to think about what's beneath the kakegoe.
I care more about the person than their kakegoe. But Kakegoe can be a tool for me to measure how a person is feeling and aim to improve the individual's spiritual/internal condition (kiai) to impact our team so that as a body, as one, we radiate an internal well-being that's good for doing what's right, what's respectful, what's kind, what's honorable and what's courageous.
I think whether we will or we won't embody these qualities of character has to do a little bit with how we are feeling. It has to do enough with how we are feeling that as leaders, it merits taking the time to invest a moment of genuine interest in how our kohai is doing and whether as a friend and role model of some sort we can do at least something small to improve their day. Sometimes, all we have to do is really recognize them as a friend, listen and welcome them to speak with confidence about what's on their mind or on some subject. Also, I ought to recognize that building up their spirit probably has less to do with saying "Kiai!" over and over and maybe a little more to do with taking action to influence their spirit positively. Hopefully, week by week, kakegoe will be even just a little bit louder than it was the week before because week by week members feel more confidence in themselves and what they can accomplish.