Recent generations of ARM-based processors in phones are doing some very fancy processing for camera phones, so in far bigger devices like an ILC with lens, especially in 36x24mm format, I doubt that the weight and cost of a powerful processor and the battery to run it are much of an issue. (And for the EVF vs OVF comparison, note that the weight and space saved by eliminating the mirror and pentaprism allow for a lot of additional battery capacity within them same "size and weight envelope"!)
BTW, the idea of adding auto-focus to a manual focus lens by moving the sensor was tried in the Contax AX, back when the sensor was a chemical emulsion on a polymer film. It made for a very bulky camera body.
You have to move a lot more stuff, including film take up spool, film canister, pressure plate, and mirror, the PDAF sensor, and also the pentaprism, etc, with the focal plane when you move the focal plane of a film camera. That's part of the reason Contax AX was so bulky. It is literally a full sized 35mm film camera inside an outer body, with the outer body big enough to give plenty of room for the inner camera to move around.
This reason doesn't apply as much to a Digital. In a Digital, all you have to move is the sensor, the shutter, and the wire ribbon leading to it. That's why you can have in-body stabilization with DSLR, and almost certainty not with film camera.
In addition, If you use mirrorless and PDAF and EVF, you don't need to move the mirror or the pentaprism. You might even get away with not moving the shutter, or even not having a shutter, if you can get your sensor to flush fast enough.
The other part of the reason why moving focal planes inside the body makes for bulky and thick bodies is with some lenses, the focal plane has to move quite a lot to cover the entire focus range of the lens. If you don't give the sensor enough range of front-back movement inside the body, then it will never find a good focus on its own. So the body would have to be much thicker than the maximum range of focus movement of any lens you plan to use with it in AF mode. Otherwise you have to manually prefocus before the autofocus will work.
So I think with a digital camera, if you do something creative, such as make the camera body deep but slim, like a compact camcorder, instead of the DSLR shape or the current SONY mirrorless shape, which is wide, tall and thin front and back, you can produce a good digital full frame camera with in-body focusing and in-body stabilization, that never needs AF lenses.