Eizo made a square 1920 x 1920 monitor which was quite nice: https://www.eizo.com/products/flexscan/ev2730q/
That looks genuinely useful - I could see positioning a monitor like that on either side of my main monitor, at an angle, and using them for docs, reference material, slack, calendars, etc. All the screen space of a dual-monitor setup, without the separation right in the center! Ah well, shame they're no longer made.
LG sells a DualUp monitor that is 2560x2880, same size as two 2560x1440 displays stacked on top of each other: https://www.lg.com/us/monitors/lg-28mq780-b-dualup-monitor
This worked great for a home arcade machine. Kind of expensive, but worked equally well for both 4:3 games (Super Mario) and 3:4 games (Pac Man).
Thanks, I hate it
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.