one inch punches are easy
Come on, there is nothing mystical about the one inch punch. It is a simple matter of learning what muscles to use. I can teach a person how to do it in 5 minutes.
It's all about pushing through with the right leg and pulling back the left shoulder. I can touch a person with my fingertips, standing in front of them feet shoulder width apart, and collapse my hand into a fist and knock them down. I can do that with a closed fist 1 inch away also. Of course, I am a 5'10" 250lbs with 31" legs, so my leg power makes it easier for me.
However, it's not this mystical and difficult thing to do.
As far as fight applications. The no inch and one inch punches teach you how to apply force at close range, it can teach you to make you jabs (and repeated jabs) more powerful, it teaches you how to develop a propper power chain, with your feet, legs, torso, and shoulder/arm. It is especially useful with arts like Goju-Ryu Karate or Isshun ryu that are based on up close techniques.
Oh, and it's fun to show your friends when they start BSing about fighting. "C'mere, lemme show you a little trick..."~Nathan