The FA and the DA lenses project an image circle onto an area
larger than the APS-C sensor (FF in the case of the FA's, APS-H in the case of most of the DA's). They have to do this because a stabilised sensor is moving up/down and side-to-side as the photo is being taken, if the image circle only "just" covered APS-C you'd have vignetting where the edges of the sensor were being shifted outside of that area.
In order to have a FF sensor with stabilisation you'd need lenses with an image circle
larger than FF, so you can discount the idea of any of your existing glass working on such a body. Canikon get away with it because the stabilisation is in each lens, not the body. Those manufacturers using in-body systems could probably make a compromise by having stabilisation work on a new even-bigger-still lens system (XLA?
) and have it shut down when an FA/etc lens is attached. Wonderful.
Personally, I think technology will overcome any shortcomings of the APS-C (or thereabouts) sensor within the next 5 years and the current FF models will be remembered as dinosaurs that tried to cling to an outdated principle well beyond its sell-by date. Just my $0.02