Part of my goal is to draw out the why an aiki model is somehow different than a ki model or a kata model, or any number of designed education methodologies..
I like that you are saying "different" rather than positing one method as better than another - I am playing with internal stuff myself, but also appreciate that aikido is a "big tent" with room for many forms of pedagogy and see no reason for disrespect of differing goals.
I have been thinking about this a lot based on my relatively limited exposure to what you are calling the "aiki model" (or internal training), working on integrating it into my aikido practice, and also as an instructor for beginners in my Low Impact class.
Personally, I find that "keep one point" (or "mind at one point"), "extend ki" etc are helpful metaphors or reminders, but in and of themselves do not explicitly teach what the body should DO in order to be able to do those things.
What I like with what you call the "aiki model" is that regardless of which particular person I have learned from (and there have been several) I'm given clear, specific instructions on how to organize my body structure and use it, in terms I can understand, based on finding pathways of intent and connection within my body and actually activating specific body parts (this is not a phenomenon specific to martial arts; my former myofascial trigger point therapist, before disappearing into the Yucatan, had me lean into my arms on a wall and touched the lowest point of my scapulae to get me to learn to be aware of and then to activate a specific muscle I'd never had any awareness of; I can now activate it with ease from any posture if I find my posture has gone "off").
I have changed my vocabulary a little to make it easier for newbies to understand - so "intent" or "energy" instead of or alongside "ki." I still make ample use of metaphors or visualizations (like fingers floating up, embracing the large beach ball behind your partner, looking at the four upper corners of the dojo, etc) because for many folks they are a quick way to get at least a temporarily improved structure, connection and movement. I'm finding that beginners who may look baffled to being told to organize their bodies around "principles" respond very well to specific directions about what to do with knees, hips, head, elbows, etc.
In terms of my own training, well, like I first said back in around 1998 or so...."my aikido sucks at a higher level"