Just testing out the ability of the Ricoh GRD IV when it comes to shooting square format.
It actually allows you to shoot RAW (DNG) in 4:3, 2:3, 16:9 or 1:1 which is quite handy.
I think there are a number of advantages with square format, the main being that you do not need to decide if you want portrait or landscape.
It could be handy for street photography if you are holding the camera at a low angle one handed, as it would be easier to hold it in "portrait" mode.
Luckily I have noticed that Rawtherapee auto corrects a photo taken with the camera in portrait mode, presumably using the orientation sensor built into the camera.