George perhaps, with utmost respect I think you are missing my point, or at least misinterpreting my words, and in essence I agree with your comments.
(I think we need to careful here, I am talking about static kihon techniques, not ki no nagare, that's has a slightly different story)
The intention of Uke is not to grab such that his/her whole body tenses and becomes stiff and rigid; and I concur the 'grip' should be directed towards nage's center (One point). You can hold a tight grip without tensing you legs, or your pelvic floor for instance. The face, the eyes will tell you everything about where the tension is being held.
When a 'beginner' is grabbed hard they usually focus on the power of the hold and hence they have a tendency to tense up themselves, and struggle to find a way out. This makes the technique hard, if not impossible to do. (This was the point I believed you made in one of your replies)
So nage is learning to move around the power of uke. The stronger the grip the better the lesson in moving around that power. Then no matter how hard (or even tense) uke becomes, nage has learnt to let go, relax, and developed a sensitivity to feel the freedom of movement that they do inevitably have, in one direction or another.
But it needs to be done progressively so that over time nage learns to 'let go' more and more, and realizes that no matter how hard or tight they are grabbed they are not trapped and there is a way out. (This for me applies to Aikido in verbal assaults too, but that's a separate thread entirely)
To quote Saito Sensei: "If you cant move when you are grabbed it isn't martial arts". The bully on the street isn't trained in how to grab nicely, they may tense up but most likely they will just hold as tight as they can to try to restrict your movements.
(This is obviously just one way of learning Aikido)
My greatest objection to the way Aikido is generally done, and it's the way I did it for years, is that the nage is attempting to do technique with total relaxation, using very sophisticated principles, against an uke that attacks like he is mentally deficient.
50% of your training is done as uke. If what you are doing in that role is different than what you are doing as nage, your body just gets confused.
There should be no difference between how you deliver a grab and how you grab someone. For many folks, it is almost the opposite as uke from what they do as nage. For many, they are indeed the same, but only in the sense that they are too tight and muscling in both roles.
I am not saying that, once you know what you are doing, that you can't move if someone is stupid enough to try to restrain your movement. I am saying that, in the hierarchy of likely situations in any martial encounter, being grabbed with the intention of holding you in place is just about the least likely. Holding someone and not letting them move will not set up a throw, will generally not create an opening for a strike, and has no function. Teaching Aikido people that this is a way to attack is doing them a disservice. Teaching them to grab i a way that can break the partner's balance at the moment of the touch is a primary and valuable skill for any martial artist and requires that nage actually be more sophisticated in his technique to avoid having his center taken.