Here's the sequence as I see it:
1. Ukemi - in the sense of falling - is a great body conditioner. And you learn to relax while taking a huge blow from the ground. And done over and over again, getting up with a centered posture, ready to "fight," trains kamae, kokyu (in the sense of aerobics), emotional centering.
2. I am only theorizing here - BUT - if ukemi/falling is coupled with specific breathing exercises - is it not possible that it, like most other activities, could become a vehicle for internal training? I believe the possiblity that this is what Sagawa might have meant. OR, he merely meant that you have to develop the right body as "vessel" to contain internal training - and he saw taking hard falls as a means to this. In either event, he - and Ueshiba - cite ukemi as essential for the development of the "aiki body." And I think they were referring to both ukemi as falling (otherwise, why, "bang, bang, bang") and in other references, to the concept of ukemi as the redirection/countering/transmuting of force.
3. Beyond this - ukemi as a vehicle for internal training - now if we talk about ukemi, not as falling, but as reception, sensitivity, getting inside the other, redirection of forces - this, I've discussed to the best of my ability in Aikido is Three Peaches, in HIPS. Dan Harden, over the years, has made some really cogent posts on this subject specific to aikido/aikijutsu.
In regards to #2. Do you think that Sagawa and Ueshiba could have been talking about ukemi as more of a progression-type of training? Working internal skills requires taking ukemi. And so, as one gets better, the internal ukemi get better (as noted in your #3). But, to get better, you still have to take ukemi of some sort.
And perhaps with Ueshiba and Sagawa, what they were taught/knew was that model from Takeda where students take falls and rolls and such? In their eyes, they knew the importance of taking ukemi (#2) because it is the vehicle (#3) for internal skills to grow. Dunno, just tossing out an idea.
Another thing that I wonder -- if the Daito ryu model was to, generally, bring uke to the feet for break/kill and Ueshiba's model was, generally, to cast away ... If we look at Ueshiba's model in a bit more detail, then do you think that rather than work within the specific model of taking uke to the feet, he was, instead, working with "following" and "changing" the energy? In other words, he was working on ways of dealing with not only regular martial artists, but also with those who had "aiki"?