I spent probably the first 10 years of my training doing flowing, primarily from motion stuff, with an emphasis on connection and timing.
Then I started training with my current teacher and working with people who offered little or no momentum and lots of resistance. Nothing I'd ever been taught before worked at all. Now when I go back and play with more flowing folks, it seems almost trivial. If you can make something work against a static opponent, it's even easier when they're in motion. My experience anyway.
I think static resistance is a training tool. No it's not how people fight, but neither is shomenuchi.
In my opinion you are spot on here. Static training teaches about proper connect, body mechanics, and it helps develop proper body structure. It should be an important part of daily training. Being the uke in static training is teaching exactly the same set of skills. The difference between being grabbed by someone who is merely muscular and one who is training and knows how to grab from his hara is vast.
The progression of practice should be as follows:
a) Static Resistive Attack - nage allows uke to grab and establish as strong a base and connection as he can; nage learns to join with the attack and give the energy new direction. Uke is merely strong but is not actively countering (meaning shifting his energy to counter)
b) Active Resistive Attack - same thing but now uke grabs but attempts to push, pull, or otherwise destabilize the nage. Nage at this point needs to connect with uke BEFORE physical contact (ki musubi). He needs to establish Ittai ka (single body) at the moment of physical contact and neutralize the partner's strength (katsu hayabi - instant victory). It is important to understand that if this is done correctly it is not a reaction to the push, pull, or whatever from the uke; it precludes those actions by neutralizing them).
Unlike the Static Resistive Attack, the Active Resistant Attack has some temporal principles functioning but if this is done at the higher levels, the feeling for both partner's should be that nage had uke before he even moved (timing should not really be an issue if it's done properly).
If this is done correctly, even though uke intends to attack strongly, he feels his focus disintegrate at the moment of contact. If one looks at what Ikeda Sensei is currently doing, it has a very heavy focus on this set of principles. I've watched the progression of his skills since the early eighties... I have been doing a video archive project and found some old seminar videos with Ikeda Sensei teaching. At that time, his technique was very strong. We'd attack him as strongly as we could but his structure was like spring steel and he could beat us every time. But at that point it was possible to at least make him work for it. Now, no matter what your intention to be strong may be, you can feel it just disappear when you make contact, instead of being string you simply find yourself moving.
"Aiki" in terms of waza is how one moves the mind of the partner / opponent in order to get him to move his body. The inputs to the partner's mind are his senses: sight, touch, hearing, and even the intuition. Most Aikido folks, as you commented use movement and timing in their technique. This is essentially using the sense of Vision to get the opponent to move himself. It's very effective in doing so but there is still the moment at which physical contact is made... Most Aikido folks don't do as good a job here. Either they use too much physical force to execute their technique or they encourage ukemi that facilitates the techniques.
Static practice, is the study in minute detail, of what should be happening when physical contact is made. If you start with Static Resistive and move to Active Resistive you basically studying how to get the opponent to move using the sense of touch. Vision doesn't have much to do with static practice and it is even very useful to have both partners close their eyes sometimes just to cut off any tendency to access vision rather than to develop the tactile sensitivity required. Anyway, this practice is more important than movement practice initially as it is the foundation for most technique.
At some moment in EVERY Aikido technique there has to be a point at which one accepts the attack. Many Aikido people use the movement of the art to avoid the attack. They cannot really execute technique because they never really join with it. Static practice puts one in a place where he or she has no choice; either join with it or be frozen in place.
Static practice is also very important for training the proper relaxed intention. Since it is low speed, low impact, it is the least threatening form of practice. One repeatedly conditions the body and the mind to have the proper level of relaxation and focus. In other words, static practice is the first step towards conditioning the body to believe that relaxing will make it safe rather than tensing.
It is also from the very the beginning that whatever solo kokyu power training exercises might be utilized should be introduced since it this type of conditioning which develops the proper internal body structure to do technique.
The next step in the training process should be focusing on movement but should really zero in on Entries and Kuzushi.
c) Entry Practice - uke should initiate the attack of choice, whether striking or grabbing; nage should practice the Entry Only, the idea being that he should now use movement (communicating with the partner largely through vision) to facilitate the physical joining of the two partners. The goal is to have the same kind of instant kuzushi which the active static practice emphasized. It is better to let the students practice their entries without any finishing technique. Their is a tendency for the student to get ahead of himself and focus on the throw rather than what sets the throw up properly. By simply doing entries, the students can focus on just one issue at a time and the once again tend to stay more relaxed. This practice can start slow and work up to full speed, never going faster than the partner can do without introducing tension (mental or physical) into the movement.
In other words, this practice has movement in the form of the entry but the moment of physical contact should be using exactly the same principles of the Active Resistive Static Practice. This way movement and proper structure are connected at all times.
d) Waza - now it's ok to start putting the elements together. Now that the foundation is laid and one has decent body mechanics and understands the entries which set up the waza, one can start practicing starting slowly and building up to full speed, full force. Don't go faster than the partner can handle because this simply imprints fear and tension. Practice must be about releasing fear and tension through the practice not the opposite.
There are other principles that need to be introduced as well as these... this is just a basic outline of how I see the progression. Focusing on movement right from the start before anyone has the structure require to handle the energy when contact is made just results in a hollow practice.