The throttle pulls on a spring connected to the govenor arm and the govenor arm is connected to the carb by a rod.
If the spring is there and moving the govenor arm but the govenor arm does not move when the engine is running the govenor is kaput.
Have a close look at where the govenor SHAFT comes through the crankcase and make sure the govenor arm is tight on the shaft.
If that is the case then off with the top plate and replace the govenor.
Very easy job on a Kohler as you can do it with the engine in place once you have removed both belts from the pulley.