To my perspective, the likelihood leans more toward the use of suwari waza being a better way to train internal methodology, than having anything to do with custom or historic connection to armored combatants. Here's why:
Proper alignment, structure and ground contact, and the absorbing, propelling and directing of force, are much easier when standing. Standing creates a more direct path from the point of contact (with an opponent/practice partner) to the point of contact with the ground. For beginners, it makes it simpler to feel the connections and alignments.
In addition, when standing, ground contact is concentrated over a smaller surface area -- the soles of the feet, the toes -- than it is when a person is kneeling or in seiza, where the contact area with the ground is dispersed across the knees, shins and tops of the feet. Doing internal method via suwariwaza thus requires much more awareness and sensitivity of what one is doing to move and direct force within one's own body, than does standing for this kind of training. Standing practice takes less sensitivity within the body to "distill" and concentrate power in and out of the ground and point of contact with the opponent. As anyone who does punching, kicking, striking, etc. would know, the smaller the surface area at the point of contact or impact, the more concentrated the force will be when delivered.
Ethan's point about suwariwaza taking away the ability of "cheating" by using superior height and mass -- and necessitating the proper use of hips -- is apt. IMO and IME. In internal training, beginners will use muscle strength and simple gravity/mass exploitation to push a technique through. Because they think they are "relaxed," and because they are not yet able to discern the difference between "muscling" and proper use of structure and internal force direction. Even intermediate-level students can easily revert to shoulder-muscle and upper-body use when training stress is increased.
More important (to me, at least), when standing it's far easier to create spiraling force from the ground, via torsion from the feet themselves. In seiza, you no longer have the feet available to work the ground, and instead must be able to do this with the parts of the body that are in contact with the ground. Again, this requires far more internal-body awareness and sensitivity.
Add to all this, that standing waza makes it very tempting for students to perform aerial acrobatics in taking ukemi. Taking ukemi from suwariwaza is not pretty or satisfying for people who like that sort of thing.
I have a feeling that, when Ueshiba saw students doing standing practice with those dramatic flourishes, he instantly saw them for what they were: people who were not seeing the (aiki) forest for the (pretty throws/ukemi) trees.
So, my conjecture/hypothesis in summary:
Waza while standing = Easier for beginners to start learning structure, energy/force manipulation, and point-of-contact.
Suwari waza = More advanced, For more deeply developing aiki and effective direction/transmittal at point-of-contact.