In the past, I have been consistently skeptical about the prospects for a square sensor camera, but maybe it is a bit less UNlikely now, due to the rise of mirrorless system cameras. The reflex mirror and VF prism are a headache for a square sensor, because, for example, going from 36x24mm to 36x36 requires a larger, heavier, noisier mirror, a larger heavier focusing screen and prism, and a deeper lens box that requires longer back focus distance on all lenses, a disadvantage for normal to wide angle coverage. On the other hand, a mirrorless system with good hybrid on-sensor AF reduces the problem to just needing a somewhat larger and more expensive sensor to get the same image size most of the time, once one acknowledges that most final displayed images are in oblong shapes from 4:3 to 16:9 (video), while square images are mostly for Instagram, Facebook, and website avatars.
Who might do it? I would guess at one of the "second-tier" companies already exploring territory other than the still-dominant SLR mainstream ruled by Canon and Nikon. Maybe Ricoh-Pentax, to move beyond the flop of the Q system and its K-mount mirrorless attempt? Maybe Fujifilm or Olympus, who keep looking around for new niches?
One constraint on cost is the 26x33mm maximum field size for fabbing a sensor without on-silicon stitching, but that would still fit with up to 24x24mm, working with existing mainstream "APS-C" lenses. I would prefer expanding an existing format, covering the whole image circle for which lenses are designed, even at the cost of some vignetting near the corners of the square with some shorter focal lengths, on the basis that those will almost alway be cropped away (like the multi-aspect ratio sensors that Panasonic used to make) but that might lead to some user confusion and complaints.
