Nikkyo - absolutely, no pain when performed properly as a connective technique that allows for Kuzushi - same with Sankyo, although admittedly it's slightly more complicated with Sankyo. But quite possible. What is called for is the skill of connecting through to Center without "disturbing anything else" so to speak.
I don't do or teach Hijishime, it's not part of my/our syllabus, nor is it in some other Aikido styles, as, if I understand the one you are referring to, it works against the joint.
This, to me, is the evolution of Aikido, although clearly O Sensei could do it when he wanted to, so in that sense it's both "progressive and regressive."
agree with you Larry, I think of it as making sure there is no slack so I am directly connected to the core of their body structure (what we call "the one-point") and able to lead them / break balance - however you want to label that feeling.
the thing is if you really are doing it well, you are capable of creating a great deal of pain instantly if you chose to, simply choosing not to because it isn't necessary and as you point out from the story of Tohei Sensei, desirable.