Upset recovery is expensive. Upset training in a light airplane won't carry over or have a lot of relevance to flying a corporate swept wing turbojet aircraft; neither will tailwheel training, etc. Helicopter training is expensive and also have virtually no relevance to flying a corporate aircraft.
Some will go get additional ratings for their own purposes. Many won't. Very few will bother with additional type ratings; most of us find that if we need to take expensive training, we'll let an employer pay for it.
Some of us flew tailwheel, did aerobatics, and and other such stuff long before we flew turbojet aircraft.
As for stick and rudder; most jet aircraft require the pilot to keep his feet flat on the floor; a little too much rudder can lead to disaster. On a big airplane like the 747, too much rudder can roll the airplane over. On most transport category aircraft, too much rudder or reversal can cause a structural failure.