My mother is an avid golfer. She says that there is an expression:
Putt for dough.
You putt when you are on the green. This is when your skills count the most. If you can minimize your putts, you will do well. This is for the "dough" (an American slang for money).
To me, koshi is like driving. In fact, using your koshi (core muscles) is necessary to drive the ball well. Using your body in a coordinated manner will increase your speed and power in golf as well as Karate. However, it is only one aspect of the game. You still have to be able to hit the ball straight, read the course, put spin on the ball, chip, and putt (among many other things).
Using your koshi will help you to move faster and with more power, but you still have to know how to hit an attacker, where to hit, how to block, parry, slip, throw, take down, trip, and many other things. Having more speed and power is like being able to driving the ball far. This is good, but no one wins in golf by driving alone. You have to be able to putt too. In Karate, you must be well rounded.
Charles C. Goodin