I had a blackberry passport and it had a lot going for it(best keyboard ever on a phone) but one thing I really liked for reasons I don't understand is it had a square screen and took square photos.

Square (or squarish) formats were pretty standard in pro photography once upon a time. Bliss, the Windows wallpaper, was shot on a camera that shoots in 6x7 natively (that's a nominal 6cm x 7cm, really it's more like 55mm x 65mm) A lot of other medium format cameras also shot in 6x7 or 6x6. And of course, 8x10 is still the standard "medium size print." I find square (or squarish) easier to compose with than wide ratios. Street photography, portraits, and sports photography don't often benefit from wider ratios, to name a few examples.

Square sensors ought to be more common because they maximize the field of view for a given lens. Well, apart from circular sensors.